It's semantics at work. I'm A/G, and even within our "fellowship" there is great conflict (low level, but still there) about calling ourselves "Protestant". The name protestant for many simply means "not-Catholic". For others it means "those who protested the Catholic Church".
You'll notice that I used the word "fellowship" rather than denomination. Again, semantics.
The A/G is a weird anomaly among major churches in the U.S. It started here, but was focused on missionary evangelism even early on. That focus has resulted in the fact that U.S. adherents to the A/G are less than 10% of worldwide adherents.
Since each nation runs it's own branch of the A/G, there is no real centralized control point for day to day workings. This has, ironically, allowed the A/G to be very active in areas that other churches have found great problems in working, such as Iran.
The A/G website has some very good information about our doctrine if you are interested.
www.ag.org