i would imagine if you called directv to come out, whoever they send will tell you they can't do the install because of the MDU account. however in that situation i guess its almost like saying, if you want to use our pre-ran coaxial cable lines, you have to go through the MDU service.
i dont see why you personally could not get a rail-mounted dish on your balcony assuming the dish has a clear line of sight. since you cant drill through your apt then your lines would have to be ran through the window using flat cable connectors and you would have lines everywhere but it would still work.. as far as your apt management seeing the dish and saying something about it, i dont know.. the problem is actually getting an installer to do it knowing you have an MDU account at the complex. you could take a gamble and call them out to come do the install and just tell the technician that you will throw him a little cash to bend the rules and have him put up the dish, or you could even spray paint that sucker just to try to hide its "directvness" lol..