Hi! Hardcore techie here. Its quite slick actually. When you enter the car, there is a handshake between the car and the iphone over Bluetooth, basically securely recognising each other, this then initiates the WiFi connection. You are absolutely correct that the data then flows over WiFi but I believe you'll still be able to find that your phone shows that it is connected via Bluetooth, even if the connection is no longer used.
Indeed, that I think is the root of the problem. The iPhone thinks its fully connected over WiFi, and doesn't understand it can't get internet bandwidth that way. Maybe its just my iPhone, hence wanting to see if anyone else had encountered the problem or found a solution!