I really like your distinction. It's definitely important to keep that caveat in mind of selfish but not at the expense of others. That's kind of my point: if everyone were "truly" selfish, they would be nice to each other.

I think everyone is selfish because they have an ego, a sense of self, like everyone is born with a stomach.

Along the idea that not everyone is selfish: there is in Big 5 Personality Theory the dimension of Agreeableness, which people can be more or less agreeable (compassionate, selfless.) But they are agreeable because social harmony is a selfish good to them-- they feel the joy of others, or the pride of self sacrifice.

But I agree that "self-interested" sounds more palatable and has more of the connotation of "...without hurting others," which is a principle I entirely agree with.

One reason why I agree is B.F. Skinner's Operant Conditioning psychology: in short, zapping mice and people with punishment just motivates them to avoid punishment, but to get them to do what you actually positively want, you have to reward them for successful behavior, so I think there's at least one scientific reason that true selfishness requires niceness.

Thanks for reading and leaving such thoughtful responses! :)