UPDATE:: Me again.
I don't have any real updates but I had a callback from Apple Support and the Support Advisor concluded that yes it was incredibly creepy but they have no idea how or why this could have happened. Their recommendation was to do a factory reset via iTunes. (This is different from doing factory reset on your phone itself). They also suggested changing my iCloud password. In reality, they believe my iPhone somehow became compromised and a full restore was the only way to fix it. I suggested throwing my phone out the window but apparently that wasn't on their troubleshooting list.