This morning at 3:30am in a hotel, my iPad 4 (iOS 7) face timed my wife all by iteslf!? WTH?
The call woke me up and sure enough, I open the case and there was my wife. I see a few others have had this problem.
The ipad was plugged in and hadn't been touched for 5 hrs at that point.
So you had one weird FaceTime call...lol. Chalk it up to a strange phenomena and move on. If it becomes a regular problem, take it to Apple...even if it's out of warranty, they'll probably want to check it out since this is not a common issue at all. They may even give you a good faith repair or replacement if there is an actual issue found.
Not to imply that this is definitely the scenario, but some cases do not activate the sleep mode properly on the iPad. My wife had a case she absolutely loved that some how always opened the last app she had open (sometimes a game or video that would make noise)...it did this because the case wouldn't properly put the iPad to sleep and it would touch the screen in a way that would access this stuff. We were in a movie and her iPad started making noise...she reached down and Plants vs. Zombies was playing on the screen.