Well, there are a lot of things that get called "consequentialism" (take a look at the SEP article for a similar point). I personally find that "consequentialism" connotes to "agent-neutral" in my head, but that may just be me. I feel like requiring neutrality is a more interesting position precisely because bare consequentialism is so weak: it's not really surprising that almost everything is a form of it.

There's also the possibility of accidental equivocation, since people use "consequentialism" to stand for so many things. I actually think the stronger interpretations are pretty common (again, the SEP article has a little discussion on this), and so there is some danger of people thinking that this shows a stronger result than it actually does.