Your words have many connotations. 'Subjective' and 'relative' are often misunderstood at the best of times. If you could taboo these, we'd see where any real disagreement lay.
Also, I don't see any more disagreement here. 'Greatest good for the greatest number' is a calculation to be made. If that statement sums up all of ethics, then it is a logical fact, not a physical one. I can't shoot your fact to make it different. We can simply turn the criterion for 'good' into a computation, so that we input physical facts, and it comes out with advice on what to do next.
Even if this morality isn't grounded in the 'nature of the universe', if this is all that we care about, then the computation is still a logical thing(y). Even if evolution adapted us to desire this, if this statement is the summation of all ethical facts, then that wouldn't change the computation. Which computation we're interested in is a product of contingent facts, physical, evolutionary ones. This doesn't change the fact, that, when we compute the greatest 'good' for the greatest 'number', we're talking about a computation that's substrate neutral. And logical.
You're probably right about the subjective/relative thing. He admits that things like this are contextually based while being marxist enough to say that the context itself doesn't matter, only that the logic is able to work within it.
Ethics are inherently logical, not physical. Obviously you can't shoot it but you can disprove their value easily enough by attacking what they're contingent on. Not all logic is created equal, and don't bring evolution into it. You can just as easily say that this is the common belief imprinted onto us by society only because the masters society us to be more easy to rule. Considering many other things, this is probably the case.
Pigliucci:
http://rationallyspeaking.blogspot.de/2013/01/lesswrong-on-morality-and-logic.html