Yeah, it is a thing, but beware also the times when you misremember both their words and your own. I, certainly, have been guilty...
At the same time, it may help to remember that people are often listening to, and I presume 'remembering' a sort of semantic meaning of what you said, not the words. Add to that a little mishearing, some assumption, and different expectations between you and them, and that can shift the meaning a lot from what you meant, while to them it seems they just approximately remembered.