My first problem with the statement (I didn't spot the tautology, and this may just be the way I read it) was that it suggested the 'people' (as the subject of the sentence) were not true (which is impossible) rather than the misconceptions not being true (which is possible, although redundant, as already pointed out).
I've been thinking about this none is/none are thing.
'None' is (obviously) an elision of 'not one', and in Old English there was a word for 'not any' - the equivalent would be 'nany', so strictly speaking 'none' should always go with a singular verb, as 'one' does (and the quote in the OP should read "Nany of them are true", tautology aside).
However, since we lack this word nowadays, and 'you' is used with both singular and plural verbs, there seems to be no reason why 'none' shouldn't serve both purposes. I'd quite like 'nany' to exist though.