Hope to see pictures of what you are conderned about. I have no personal experience with a LAQ, but I would be very upset if there were folds in the backing of my quilt. Some of that may have been avoided by asking her to show you what she meant by the puckering. I would never take a quilt home without looking at it when I picked it up.
I work with hand quilters at church,and we always open up the quilt when the person picks it up (so we can all ooh and aaah with the quilter!) We are not always 100% successful, but we know if there is a problem immediately! And we have the option to make any adjustments right then and there. :?