Exactly. The only assumptions that economics makes about people are that (1) people have different utility functions and (2) that they rationally pursue them. (1) is satisfied even if everybody is perfectly selfless just as much as if they're perfectly selfish, it's only if everybody was a perfect utilitarian that it would break down. (2) is much more tenuous but usually works well enough when you're dealing with large number of people who can try different strategies and adjust their approaches depending on the success of their friends and neighbors.
I think (1) is a tenuous assumption as well, especially in some formalizations. Cardinal utility (the idea that it makes sense to say "I want X lambda times as much as I want Y") is almost certainly bunk. Even assuming a total ordering seems unlikely.
They make a lot more assumptions than that, neoclassical economists at least. How do you think they manage to aggregate the preferences of millions of people to provide "microfoundations" to their models? See the aggregation problem on wikipedia.
