There's room for some confusion as to who commits the fallacy. If the speaker correctly classifies a mistake (that really is a mistake) as part of a category of structurally related mistakes, that's hardly a fallacy. The fallacy is, as you point out, taking a nice sounding label itself as evidence. Using quotes from famous people creates a similar danger.

I think there is a name for this effect, "association" or "framing" or something. But whatever.