It's a bit beside the point here, but what's the deal with American outlets always referring to a specific brand name version of one of the most generic drugs?

Because that what most people call it. It's just like calling tissues Kleenex.

Media is saying "Tylenol" because that's what the President kept saying. He had to say "Tylenol" because he can't pronounce "acetaminophen".

The term has become genericized, like Kleenex or Hoover.

Drugs are advertised heavily on TV here, so they use the names people know.