While you're technically correct that intent and interpretation are entirely independent, if you throw away all context of the statement and frame it in your own pedantic and literal interpretation...why are you even engaging in communication? You obviously aren't putting forth any effort to understand the speaker's intent and that seems to be at the heart of conversation and debate alike.
My point is not to throw away the speaker's intent, my point is that the speaker's intent is only one factor in how people will interpret what is said.
For example if I say "She sure is smart for a girl." I may not be intending to be a misogynistic asshole, I may be intending it as a compliment. But most people are going to read it for what it is; a comment that shows my own bigotry and means nothing outside of that.
Not when your interpretation seeks to define the other person's statement to fit your viewpoint. You can respond with:
"You seem to be saying this, and I think that's wrong. Is that what you're saying?"
versus:
"You are saying this, and you are wrong."
It's called communication. It's a two-way street.
If the speaker intends a statement as a compliment but states it badly, why is your reaction that much more important because you take it as an insult? Why do you get to redefine the intent and totally dismiss the statement altogether, which means you are also dismissing the intended compliment?
That type of reaction actually increases the misunderstanding and makes the problem worse in the long run.