Yes!! I have this problem, too! Had this happen a month ago - somewhat entertaining, actually! - but when I reported to AppleCare chat they suggested that since my warranty would expire in a month, I should take it to the AppleStore for a possible replacement. And I did get a replacement. The new phone did the same thing! So I went back yesterday for the third new phone, and yes... this one's haunted, too.
I agree with the commenter that it only seems to happen when it's connected to the charger cord - and to an outlet, not to a computer. Previously, it has opened random apps, tried to enter passwords (dots, so I don't know if the passwords are correct or not), and tried to make a phone call - all while I was watching and not touching/holding it. Now, I can wave my hand across it, hovering about 1/2" from the screen, and it moves from app to app, scrolling up and down the page... weird. So, I'm here searching for a possible sensitivity setting. I found where the 6S has a setting, but can't find it for the 6. Help?
I'll try adjusting the setting before contacting Apple again.