Some AGPS devices cannot determine their own position from a satellite signal, whereas others can as long as they have received an almanac from a server in the recent past. It depends what you mean by "actual GPS". Some implementations are completely incapable of acting in a standalone capacity.
Here is what the Wikipedia article you linked to says: "Standalone" or "Autonomous" GPS operation use radio signals from satellites alone. A-GPS additionally uses …
I don't see how this contradicts what I said, which is that some AGPS implementations require assistance in order to accurately determine your location. Not every AGPS device can map radio signals to a lat-long; some can only do that with assistance.
It also lists some ways that various implementations require assistance:
Assistance falls into two categories:
Information used to more quickly acquire satellites
It can supply orbital data or almanac for the GPS satellites to the GPS receiver, enabling the GPS receiver to lock to the satellites more rapidly in some cases.
The network can provide precise time.
The device captures a snapshot of the GPS signal, with approximate time, for the server to later process into a position.
Accurate, surveyed coordinates for the cell site towers allow better knowledge of local ionospheric conditions and other conditions affecting the GPS signal than the GPS receiver alone, enabling more precise calculation of position. (See also Wide Area Augmentation System and CellHunter and openBmap.)
Calculation of position by the server using information from the GPS receiver
The assistance server has a good satellite signal, and plentiful computation power, so it can compare fragmentary signals relayed to it
That’s not what the article says. It says that AGPS devices are just like GPS devices. The only difference is that they use additional information to improve startup times.
Assistance is described as something that’s entirely optional. Why do you think that’s not the case? I googled around for a bit and it seems as though every source I can find tells me that AGPS is just like GPS if you have no data connection.
I'm sorry but I don't know how to make it more clear than I already said before: some AGPS implementations are not capable of operating in standalone mode. The Wikipedia A-GPS article states:
A typical A-GPS-enabled receiver will use a data connection (Internet or other) to contact the assistance server for aGPS information. If it also has functioning autonomous GPS, it may use standalone GPS, which is sometimes slower on time to first fix, but does not depend on the network, and therefore can work beyond network range, and without incurring data usage fees.[3] Some aGPS devices do not have the option of falling back to standalone or autonomous GPS.
I've added emphasis. The last point is all I was saying.