I don't know a lot about the technology, but I think this is correct.
I have experimentally determined that our phones are, in fact
using A-GPS
Indoors, using
VisualGPSce, I was seeing 4-5 satellites with a steady fix.
I then turned off the phone (flight mode), and rebooted. I saw 1-2 satellites in and out without obtaining a fix.
Turned the phone on and booted again with service (2 bars). Within a short while, VisualGPSce finds 5 satellites and a fix.
Thus, it seems to me that with the phone on, the cell towers are chiming in, and A-GPS is being used, being able to get a stronger, quicker fix indoors.