Heh heh. This is one of those horrible/delightful dilemmas a writer comes across: do you go with what you know is true, or what everyone (including both your audience and your character) believes? Closely related to The Tiffany Problem, though not identical. Each case is different, but I think this time going with the common error is the right choice.
Oh yeah, tell me about it! My counterpart and I are constantly having debates about that in our own story-writing. Or, well, dispassionate discussions about it at any rate. Either way, it's a right difficult choice when it comes to dialogue and grammar! Most people simply do not bother with the whole "Never end a sentence with a preposition" thing, but as a writer you have to keep that in mind or people just
will not be able to take you seriously.
...But at the same time, as I just said,
most people hardly care at all about such details. So when you write intentionally "incorrect" character dialogue to make it feel more naturalistic, yet the narration / prose is grammatically correct, it comes across as really weird and inconsistent. Which of course creates the dilemma... So many people assume writing is easy. It really is anything but.
-Mal