I know the sharp lip of the inner quarter has to lay flat or it can cut the top.
Yes, this must be done. And to repeat John's comment, my body guys were literally bashing those over on my '67 with a sledge. I remember them saying "we were wondering why those were bent over"...
This all happened the moring I was picking up the car after a frame off resto! Duohh!
If your rear inner and outer wells have been replaced, its likely this is the issue because the lips need to be bent over after they are welded. (or they won't leave room for the top to tuck down into)