In most cases, you have the single as the main song and on the other side (the B-Side of a vinyl record) you have another song to fill up the space. With a double A-Side, by contrast, the idea is that the two songs (one on each side) are to be considered as equally important. Both are being released equally as the single.
In the 60's & 70's a record company would release a 45 and promote the "A" side, then DJ's would flip the record and start playing the "B" side. The company would then list this in the music press & charts as a double "A" single. More often than not this happened by chance as record companies don't waste songs they consider could become hits on the "B" side.
Although I think the nugget is probably correct in many cases, I can think of a number which I am sure were released as double A sides. How about Rod Stewart (The Killing of Geordie) and Wings (C Moon). But I may be wrong! ;-)