I had a bullmastiff before my yorkies. I NEVER took him outside unless he was on a harness and leash (his fat neck made it easy for him to slip a collar off over his head). Of course, I never take my yorkies outside unless they are on a harness and a leash either. My bullmastiff was well-trained (these are "fun" tricks):
Anyways, I would complain. It seems like if they just kept the door to their apartment closed that would solve a large majority of the problem. I guess they aren't worried about anyone just walking in? I'm fearful the rottie may hang himself. It's so sad. These giant breed dogs really do just want the same love and companionship as the little ones, but people feel the need to treat them so differently.
I firmly believe it's bad owners (like your neighbors) that give these breeds a bad rep.
I wanted to add bullmastiffs/mastiffs, especially over the age of 2 do quite well in an apartment setting, because they generally don't have the desire to be very active, save for a few daily walks. I'd imagine the breed restrictions has to do with the apartment complex's insurance policy, though I never had an additional premium on my renter's insurance for my big guy - they only wanted to know if he'd ever bitten someone (NO!).