Misquote

[Monty]

To correct someone, with a [self-righteous] attitude, on [trivial] and technical facts, which are irrelevant to the main point of the conservation.
Misquoters are [pedantic] and often annoying. A surprising amount of joy can be had when the misquoter makes a mistake in his self-righteous misquote. (See examples.)

[Britney]

Quote (a person or a piece of written or spoken text) inaccurately.

[Sarah]

to repeat something someone has said in a way that is not accurate: