Stop.
A-GPS does NOT use cell towers for triangulation. GPS uses satellites. Period.
The only difference with A-GPS is that the phone can get assistance (the "A") obtaining information about the satellites in view and their orbits. This is normally received over many minutes from the satellites themselves. Assistance cuts that time to mere seconds. Cell id can also help with a vague starting location, but is not necessary for GPS to work.
The satellite info assistance can come from the carrier over signaling channels, or over the internet via a data channel. Depends on the implementation.
After the initial assistance, most smartphones go into standalone GPS mode until they need updated sat info again (a few hours).
If GPS or A-GPS cannot get a lock on enough satellite signals, then the phone could resort to cell id or wifi locating... or the carrier in some cases will use towers for locating (especially for E911)... none of which are A-GPS.
In the case of Google maps, data access is needed to download the images.