Why do I get the feeling I'm misusing the word "factoid?"

Because you are. If you ask the average person, the word "factoid" means "a brief, somewhat interesting fact." But, in reality, the word "factoid" is meant to describe a bit of unverified or inaccurate information that gets thrown around so much, usually through some kind of press, that its very repetition eventually cements it as an accepted fact. The seemingly agreed-upon definition of "factoid," then, is in itself something of a factoid.

If this is all too much to handle right now, just try to remember that the "-oid" suffix means "resembling, or having the appearance of." Like when you hear a human-looking creature being referred to as a "humanoid." Think about what that makes a "factoid."

Cheers,
Diego