In some cases, the misquotation is just a simplifying paraphase that doesn’t change the meaning, to present the crucial material succinctly. e.g. “Do you feel lucky, punk?”
I note that what the speaker says in this clip doesn’t match the words on the screen in the case of “Magic mirror, on the wall, who’s the fairest one of all.”
The status of the Armstrong quote is disputed. According to snopes, Armstrong has conceded that he flubbed the line: he did actually say, “One small step for Man...”. He had meant to say “for a man” but fucked it up.
Facebook seems to be a very ready medium for the spreading of mucked up, misattributed or completely bogus quotes.
EDIT: Retrocorrected thanks to Techie’s vigilance.