>Americans don't understand buying lunch for your superiors.
More wealthy/higher ranking/socially powerful/popular/lucky != superior.
I occasionally buy lunch for my friends and co-workers out of mutual respect and a genuine desire to show them that the relationships we share are appreciated. If one of them happens to be my supervisor, so be it. But there has to be a mutually respectful relationship between us.
I'd also have to seriously question the character of anyone who, being aware of the fact that they make multiple times your income, would still allow you to buy them lunch (Unless it was a trivial amount).