I, of course, totally buy that most Americans don’t know who Fred Thompson is, but would recognize his face from TV or the movies.
That said, when given the “Nothing/not familiar with,” I could see a stickler answering that way because they know who he is but not a darn thing about his politics. And even among people in the know, I still hear a lot of “was he a conservative senator? I don’t remember.”
I do think more people are probably the former, but the latter exists — and in the Beltway.