I think a more accurate version of this is: unit tests were not only per-method but also per functionality. This was often called BDD (Behavior Driven Development), e.g. Ruby's cucumber. Your intuition here is correct though.

I disagree with the "not only". The idea in xp is to write the test first. http://www.extremeprogramming.org/rules/testfirst.html You don't know how many methods/functions (if any) you're going to add to make it pass, so they're explicitly per-functionality.