This may well be a valid point in general, depending on the algorithm, but I am not sure that applies to a quine, which can only ask (and answer) one question.

What do you mean? Assuming that a quine can only answer a question about the source code (admittedly, the other commenters have pointed out that this assumption doesn't necessarily hold), how does that make the point of "the source code alone isn't enough to represent the whole system" inapplicable to quines?

And it is certainly different from your original objection about machine registers and such.

I don't follow. Machine registers contain parts of the program's state, and I was saying that there are situations where you need to examine the state to understand the program's behavior.