Okay, so I'll second the original post.
My wife's iPhone 5 64GB white had the problems since immediately after upgrading to iOS 7. No change after updating to 7.0.2.
My own iPhone 5 64GB black had no such problems for quite a while (even after upgrading to iOS 7) and only started cheek-dialling after updating to iOS 7.0.2.
Intermitting problem for me (only had it once as far as I can tell), constant problem for my wife on every single call. No cases, Artwizz screen protectors. But - the protectors have been applied well before updating to iOS 7 and have never caused any problems on iOS 6.
Oh, and, please refrain from pointing to resetting, going to Apple or anything alike. Since the phones did not have problems under iOS 6, there's no use in exchanging the phones. Resetting while keeping the firmware in place won't fix the problem either.
Basically, this post is to let Apple's support staff see that this is no longer an isolated One-in-a-million problem, but rather commonplace.