Now don't send those quilt police my way, but I always STRETCH my binding as I'm putting it on. At least a little.
The quilt I'm working on now is quite non-traditional. It has a double knit back and the same double knit squares in the top with other cottons. Just some fabric I wanted out of the house and it will be donated. I used pieces of batting, and machine quilted it in a large meander to keep these in place.
I will stretching this binding quite a bit to make the knit behaves.