I've been known to tell my customers that they don't want me to mount their amp to the box, but my reasoning is different from what I hear on the internet all the time. I don't like amps on MOST boxes because MOST installs aren't permanent fixtures in the vehicle like brenzbmr's. In most situations where there is a box just placed into a vehicle's trunk I don't like the possibility of "one stop shopping" for the thieves. They grab your box w/ the amp attached and go. The other reason I don't like that type of install is all the exposed wiring when the install could likely be much cleaner with concealed wiring on the back of a seat or something.
Now, what I always hear people say about mounting an amp to a sub enclosure is that you'll cause damage to the amp from all the vibrations as the sub pounds away.

Think about that for just a second. If a box is properly secured (and I hope everyone's is!) how much does the box actually vibrate!? I say not at all or at least very minimally. Some of you might disagree with me, but think about it in the context of an install such as brenzbmr's. With an enclosure that's constructed into the vehicle such as this it essentially becomes a part of the vehicle's solid structure. How would mounting it to the box (as is being done) be any different than mounting it securely to another solid piece of the vehicle that is in turn securely fastened to the enclosure itself

No difference at all.
IF you're worried about vibration caused by the subwoofer enclosure use a few rubber spacers between the amp and the surface it's being mounted to, whether that's the back of the enclosure or anywhere else in the vehicle.
Oh wow, I really rambled on that one! I guess it's just one of those car audio misconceptions that will never go away and I let it get me all wound up!
Back to the topic of brenzbmr's wonderful install!