Yes, it's normal practice to baste the edges as you go. Also, he may need to practice a bit to get the tension on the backing correct. Too little and the backing may pucker, too much and the top puckers. I think there's a tendency to have it too tight. As Cindi said, there's a learning curve with any tool.
I would first pin the edge, distributing the fullness as best you can. Then machine baste about a quarter inch in using a longer stitch (3, or 3.5). If you have a walking foot, this is a good place to use it. You may not be able to avoid a few pleats, but I wouldn't stress too much. the quilt is lovely and will be loved. The 2nd photo shows you have some extra batting. I would use some scraps of fabric and batting to determine if you need to go to a 2.5" binding strip. I think you may be surprised at how much the batt will compress after you machine baste it.
You have to admit those fishies are really cute, and give him an "A" for enthusiasm. Although it might be a delicate situation, he does need to be told, and know that things will improve with practice. If they bought the unit new, the dealer should offer free classes also, Handi Quilter has lots of great videos on their site:
http://www.handiquilter.com/videos/