Dedicated criminals will be promoted by the player to have all the upgrades intended for their purpose, specifically troublemaker and possibly commando (if they didn't already start with that promotion), while strike teams will end up with anything that increases withdraw chance, and probably first strikes. So entwining their upgrade paths could lead to angst in that department.
The hidden nationality thing...it depends on how you see strike units in general. I always thought of them as official high-tech highly-trained military teams who might not wear dogtags, and might do some shady stuff that could be embarrassing to their government if brought to light, but it's still pretty clear which country they're from if you recover a body. So they're never used to strike directly at the forces of a sovereign power unless both parties are at war.
A strike team should be able, just as a "purely random" example, to enter the territory of someone you're not at war with but don't have open borders with, and take out a highly promoted hidden nationality unit hiding in a town, winning international acclaim and respect, and then run back to friendly territory in the same turn. But if that team had attacked official assets belonging to the military of that non-hostile nuclear-armed country, it could have been exceptionally bad.
Then again you see units that, if they fit any C2C description, could be described as strike teams, going into other peoples' territory and assisting rebels that are trying to help them annex territory, without absolute modern warfare between the two countries.