Not hyperbole. There's a legal concept in the USA of "common carrier", holding an agent transferring information not accountable for the information transferred. As in: Verizon is not a culpable party if you use their cellular network to arrange a capital (or other) crime.

By stating content limitations in the EULA, and by actively searching for violations, MS is now legally culpable for content which is in criminal violation of the law.

Whether they are prosecuted may be a different story, but the legal culpability remains.