The UMP trigger group uses a sear as a secondary safety (even on the FBI or semi-only trigger groups). Now the area that the sear would fit into in the USC receiver is blocked, and the ATF has stated that cutting that area open is manufacturing a machine gun (big no-no). (since the sear is also used for the auto function on the Navy and SEF trigger groups)
If you take the sear out then you can use the trigger group fine, but you are missing a safety component.
The USC trigger group uses a different style of secondary safety (that also lessens the trigger pull weight) and doesn't require the cut. Since the USC and UMP use the same pin locations (except for the sear pin which doesn't get used by the USC parts) you can just swap the parts the retain all the safety features of the USC trigger parts!