Necessarily? I'd assume a factoid has the potential to be either true or false.
By some original definition of the word they are necessarily false. Usage seems to have shifted to ‘small fact’ though
The common misunderstanding of the word `factoid` to mean "a small fact" is itself a factoid.
Oxford English Dictionary (via Google) gives:
Factoid
- a brief or trivial item of news or information
- an assumption or speculation that is reported and repeated so often that it becomes accepted as fact