In the WiFi Advanced settings, there's an option for "Always allow scanning". That options description states that Google Location Services and other apps can scan for WiFi even if WiFi is off. To me, this reads as WiFi is still on, but in a low power mode; otherwise how will your phone know that WiFi networks are available. I could be wrong on how this works, but that could be a reason why your WiFi is turning on.
On Verizon, the "Smart network switch" apparently does what Rowlette mentions above. That to me seems the most plausible reason if that option is set to On.