This gets difficult, because there's a whole set of related terms I suspect we aren't quite using the same way, so there's a lot of underbrush that needs to get cleared to make clear communication possible.
When I'm trying to be precise, I talk about experiences providing evidence which constrains expectations of future experiences. That said, in practice I do also treat clusters of experience that demonstrate persistent patterns of correlation as evidence of the state of external systems, though I mostly think of that sort of talk as kinda sloppy shorthand for an otherwise too-tedious-to-talk-about set of predicted experiences.
So I feel reasonably comfortable saying that an experience E1 can serve as evidence of an external system S1. Even if I don't actually believe that S1 exists, I'm still reasonably comfortable saying that E1 is evidence of S1. (E.g., being told that Santa Claus exists is evidence of the existence of Santa Claus, even if it turns out everyone is lying.)
If I have a whole cluster of experiences E1...En, all of which reinforce one another and reinforce my inference of S1, and I don't have any experiences which serve as evidence that S1 doesn't exist, I start to have compelling evidence of S1 and my confidence in S1 increases. All of this can occur even if it turns out that S1 doesn't actually exist. And, of course, some other system S2 can exist without my having any inkling of it. This is all fairly unproblematic.
So, moving on to the condition you're describing, where E1 causes me to infer the existence of S1, and S1 actually does exist, but S1 is not causally entangled with E1. I find it simpler to think about a similar condition where there exist two external systems, S1 and S2, such that S2 causes E1 and on the basis of E1 I infer the existence of S1, while remaining ignorant of S2. For example, I believe Alice is my birth mother, but in fact Alice (S1) and my birth mother (S2) are separate people. My birth mother sends me an anonymous email (E1) saying "I am your birth mother, and I have cancer." I infer that Alice has cancer. It turns out that Alice does have cancer, but that this had no causal relationship with the email being sent.
I am comfortable in such an arrangement saying that E1 is evidence that S1 has cancer, even though E1 is not causally entangled with S1's cancer.
Further, when discussing such an arrangement, I can say that the brain-states caused by E1 are about S1 or about S2 or about both or neither, and it's not at all clear to me what if anything depends on which of those lexical choices I make. Mostly, I think asking what E1 is really "about" is a wrong question; if it is really about anything it's about the entire conjoined state of the universe, including both S1 and S2 and everything else, but really who cares?
And if instead there is no S2, and E1 just spontaneously comes into existence, the situation is basically the same as the above, it's just harder for me to come up with plausible examples.
Perhaps it would help to introduce a distinction here. Let's distinguish internal evidence and external evidence. P1 counts as internal evidence for P2 if it is procedurally rational for me to alter my credence in P2 once I come to accept P1, given my background knowledge. P1 is external evidence for P2 if the truth of P1 genuinely counterfactually depends on the truth of P2. That is, P1 would be false (or less frequently true, if we're dealing with statistical claims) if P2 were false. A proposition can be internal evidence without being external evidence...
Summary: There are claims that Boltzmann brains pose a significant problem for contemporary cosmology. But this problem relies on assuming that Boltzmann brains would be part of the appropriate reference class for anthropic reasoning. Is there a good reason to accept this assumption?
Nick Bostrom's Self Sampling Assumption (SSA) says that when accounting for indexical information, one should reason as if one were a random sample from the set of all observer's in one's reference class. As an example of the scientific usefulness of anthropic reasoning, Bostrom shows how the SSA rules out a particular cosmological model suggested by Boltzmann. Boltzmann was trying to construct a model that is symmetric under time reversal, but still accounts for the pervasive temporal asymmetry we observe. The idea is that the universe is eternal and, at most times and places, at thermodynamic equilibrium. Occasionally, there will be chance fluctuations away from equilibrium, creating pockets of low entropy. Life can only develop in these low entropy pockets, so it is no surprise that we find ourselves in such a region, even though it is atypical.
The objection to this model is that smaller fluctuations from equilibrium will be more common. In particular, fluctuations that produce disembodied brains floating in a high entropy soup with the exact brain state I am in right now (called Boltzmann brains) would be vastly more common than fluctuations that actually produce me and the world around me. If we reason according to SSA, the Boltzmann model predicts I am one of those brains and all my experiences are spurious. Conditionalizing on the model, the probability that my experiences are not spurious is minute. But my experiences are in fact not spurious (or at least, I must operate under the assumption that they are not if I am to meaningfully engage in scientific inquiry). So the Boltzmann model is heavily disconfirmed. [EDIT: As AlexSchell points out, this is not actually Bostrom's argument. The argument has been made by others. Here, for example.]
Now, no one (not even Boltzmann) actually believed the Boltzmann model, so this might seem like an unproblematic result. Unfortunately, it turns out that our current best cosmological models also predict a preponderance of Boltzmann brains. They predict that the universe is evolving towards an eternally expanding cold de Sitter phase. Once the universe is in this phase, thermal fluctuations of quantum fields will lead to an infinity of Boltzmann brains. So if the argument against the original Boltzmann model is correct, these cosmological models should also be rejected. Some people have drawn this conclusion. For instance, Don Page considers the anthropic argument strong evidence against the claim that the universe will last forever. This seems like the SSA's version of Bostrom's Presumptuous Philosopher objection to the Self Indication Assumption, except here we have a presumptuous physicist. If your intuitions in the Presumptuous Philosopher case lead you to reject SIA, then perhaps the right move in this case is to reject SSA.
But maybe SSA can be salvaged. The rule specifies that one need only consider observers in one's reference class. If Boltzmann brains can be legitimately excluded from the reference class, then the SSA does not threaten cosmology. But Bostrom claims that the reference class must at least contain all observers whose phenomenal state is subjectively indistinguishable from mine. If that's the case, then all Boltzmann brains in brain states sufficiently similar to mine such that there is no phenomenal distinction must be in my reference class, and there's going to be a lot of them.
Why accept this subjective indistinguishability criterion though? I think the intuition behind it is that if two observers are subjectively indistinguishable (it feels the same to be either one), then they are evidentially indistinguishable, i.e. the evidence available to them is the same. If A and B are in the exact same brain state, then, according to this claim, A has no evidence that she is in fact A and not B. And in this case, it is illegitimate for her to exclude B from her anthropic reference class. For all she knows, she might be B!
But the move from subjective indistinguishability to evidential indistinguishability seems to ignore an important point: meanings ain't just in the head. Even if two brains are in the exact same physical state, the contents of their representational states (beliefs, for example) can differ. The contents of these states depend not just on the brain state but also on the brain's environment and causal history. For instance, I have beliefs about Barack Obama. A spontaneously congealed Boltzmann brain in an identical brain state could not have those beliefs. There is no appropriate causal connection between Obama and that brain, so how could its beliefs be about him? And if we have different beliefs, then I can know things the brain doesn't know. Which means I can have evidence the brain doesn't have. Subjective indistinguishability does not entail evidential indistinguishability.
So at least this argument for including all subjectively indistinguishable observers in one's reference class fails. Is there another good reason for this constraint I haven't considered?
Update: There seems to be a common misconception arising in the comments, so I thought I'd address it up here. A number of commenters are equating the Boltzmann brain problem with radical skepticism. The claim is that the problem shows that we can't really know we are not Boltzmann brains. Now this might be a problem some people are interested in. It is not one that I am interested in, nor is it the problem that exercises cosmologists. The Boltzmann brain hypothesis is not just a physically plausible variant of the Matrix hypothesis.
The purported problem for cosmology is that certain cosmological models, in conjunction with the SSA, predict that I am a Boltzmann brain. This is not a problem because it shows that I am in fact a Boltzmann brain. It is a problem because it is an apparent disconfirmation of the cosmological model. I am not actually a Boltzmann brain, I assure you. So if a model says that it is highly probable I am one, then the observation that I am not stands as strong evidence against the model. This argument explicitly relies on the rejection of radical skepticism.
Are we justified in rejecting radical skepticism? I think the answer is obviously yes, but if you are in fact a skeptic then I guess this won't sway you. Still, if you are a skeptic, your response to the Boltzmann brain problem shouldn't be, "Aha, here's support for my skepticism!" It should be "Well, all of the physics on which this problem is based comes from experimental evidence that doesn't actually exist! So I have no reason to take the problem seriously. Let me move on to another imaginary post."