Binding off at the end of a row leaves your yarn at the end of the bound off stitches. I guess if it's really, really important to you, you could bind off at each end, cut the yarn, and rejoin at the last stitch before the bind off. It sounds too complicated to me. I seriously doubt that the difference is going to be noticeable. Your friend is correct in pointing out the small difference in measurement, but if you check your row gauge I think you'll find you get more rows to the inch than stitches so it's even smaller.
That's a cute pattern.
Denial, anger, bargaining, depression, acceptance...the five stages of frogging.