Erm, you actually can talk about the modal american in the same sense as any of those other measures of central tendency.
You don't talk about "the average american" with no context. You talk about the average american salary, the average american number of occupants of a household, and so on. Same for median.
The modal American salary would be the dollar figure which has the most americans earning that exact amount. It's fine.
I didn't intend to mock the average American Joe, it's just that the question doesn't make sense and I'm curious of what they wanted to know, or if I'm the one missing something.
It's normally worded "the average American makes $x a year." Who is the average American? That should actually be worded "the average American salary is $x." That's actually what's being discussed. Assuming we continue the same trend in language, the OP is correct. You're also correct, but they're saying the same thing as you, just with the poor word choice from the other things.