True...if you look at the actual circuit itself you'll see that yes they are in fact gain controls for the amplifier's "pre-drive" section. The power amp section itself has a fixed amount of power gain and it requires X amount of input signal to reach full power out, and the required amount of signal to accomplish that is determined by the fixed power gain of the amp itself. However, the input signal at the input of the amp will determine how much gain the pre-drive needs to add to the signal to reach that required value. The more clean signal you have from the board, the less gain required from the pre-drive section to get the amp to swing to full output voltage, which is why the controls are never ran full up.
However...there was a very legit reason for leaving that fact out of my explaination.
When teaching a 'newbie' (after all, this is in fact FAQ for the live sound newbie), I don't prefer to teach them that concept as it overcomplicates things for the novice. It's much simpler to comprehend for the novice by simply explaining them as adjustable input pads.
Another reason why you don't explain it to the novice like that is because to most novices I've encountered, in their mind the term "gain" = "volume" and that's not the case. I've found that when teaching someone from scratch, my first goal is to get the false pretense that gain=volume out of their heads...it leads to the "I want more volume so I add more gain" mentality that leads to disaster everytime. I always teach that gain is a measure of amplification factor and that the channel's preamp in most "club/weekend warrior" setups has more than enough gain to drive the signal through the mixer and driverack all the way to the amplifier without having to add it downstream of the channel preamp at different points in the signal path. It's always much better to add as much clean gain as possible at the mixer channel's trim control upstream of the driverack and amplifier and only have to add a little at the amplifier, than it is to set your mixer channel gain low, then have to add additional gain at the amp itself by running the amp's controls full up.