More and more often I hear people saying and see people writing "factoid", by which they mean
I know I'm fighting a losing battle on this, and that grammatical and linguistic drift will overwhelm me in a sea of inconsistencies and lost opportunities, but as Sky Masterson says to Nathan Detroit, "You can fight it Nathan, you can fight it."
Of course, he turns out to be wrong ...
I think that my use of "factoid" triggered the above, although obviously it was an existing pet peeve. However, you mistook what I meant. I did not mean "a small fact" when I said that a student may have heard "i = sqrt(-1) as a factoid", not at all. I meant that they heard it and believed it but didn't understand it; if they understood why it was true, it would be a fact to them, but as it stands, it is merely a factoid to them. This is consistent with common usage of "factoid"; the word does not necessarily mean something false, it means something treated as a fact, and which may or may not be.
Compare with "humanoid", which does not necessarily mean "non-human". If some Star Trek character says "I saw a humanoid shape in the shadows; it was hard to see, I'm not sure if it was a human or not.", that is perfectly fine usage, and they are not contradicting themselves. The shape was human-like, and may or may not have been human, and "humanoid" fits perfectly there.
Be careful who you fight your language maven "losing battles" with; some are more heavily armed than others. ;-)
Right on many, but not all counts. Your point is correct, technically "factoid" does not of itself mean it is necessarily false nor necessarily false. It was not, however, your use of "factoid" that provoked this response. I did not see your use in the sqrt(-1) context. My point is that it is invariably used in a way that makes it clear the speaker/writer thinks it's true.