Because it's code for "(originally) written on the birth certificate", which stops arguments about who gets to decide and when.

I think you're being a little too cavalier with the distinction between who one is physically and who one is mentally--at the very least it's an issue around which one could reasonably have a robust debate.

But I agree that "assigned" implies a view of the matter that is a poor model of reality, and that at least in part it's done because it's a poor model of reality (with the error in a direction that the advocates find convenient), which may be sufficient grounds for calling it a lie.