Common misconception.
Locating by Google tower database or Skyhook WiFi database, is not A-GPS. They are simply alternative methods.
A-GPS is, as the name implies, about using GPS. It consults an assistance server to get current satellite information (instead of downloading slowly from the satellites themselves). This greatly speeds up the time to first fix.
And if you want to get really pedantic, PoitNarf's statement is not actually in conflict with such a mechanism.
It must
use some form of external data communication to download the current satellite information. The only two mechanisms available to perform such communication are by
using mobile phone towers, or by
using WiFi.
Don' forget, too, that some other forms of assistance are also collectively covered by the terminology "A-GPS".
For example, if, due to poor reception, a device is only able to collect a garbled signal from nearby satellites, it can send whatever information it is able to gather back to a central service, which uses that incomplete information, along with its knowledge of the current state of the satellite constellation, to determine which satellites the device is actually communicating with, and then perform the necessary computations to send back to the device. This may not be the way in which the iPhone's A-GPS system works, but it is recognized as a legitimate form of A-GPS.
Another example: A device may not have adequate computational resources available on-board to perform the mathematics required to determine position based on the received GPS signal. It may send the complete GPS signal back to a central service, which performs the math and sends the result back to the device.