It is true. You won't be able to go online if you modded your XBOX/Playstation, though the misconception is that all you need is an original game. Even if you have an original game, you would still not be able to go onilne if your system is modded.
Having said that, it's not going to stop me from using a mod anyways. This is because I don't care for playing immature people when online. Battle.net comes to mind.