Well I guess I'll jump in here with my 2 cents. I have had this happen to me in both cases, square and unsquare. I quilt my sister quilts for her and none, I mean none of them are square and she says she doesn't care, just quilt them. Now you can guess who has the problem trying to make theses monsters look good! Her quilts were not pieced with care and she didn't care. They almost always bowed in the center. And some, no matter what I did I could not correct this. Some were worse than others. I have quilted her quilts attached and floating, it doesn't matter, same result.
Now, I have some other quilts that are pieced about as perfect as can be and I have almost no problems with them. The piecer prides herself on her work and it shows. It is a pleasure to work on her tops. Once in a while I will get one that the corners try to be longer as I go down the quilt. I watch that and ease those a little bit with each roll and by the time I get to the bottom, I'm back square.
All that being said, I don't think my leaders are square, even, or what ever you call it. After pinning, if I run a straight line across the top I will run off the top at the end. Putting on binding I cannot use a lock for the stitching because I will have too large of a seam or run off the binding. I think the leaders are some of the problem, but it has A LOT to do with the top itself. Not only it being square but if there is any fullness in the top. Now that, to me, is more of an issue and probably the culprit, than square.