You're reminding me of Night Heat in your opening paragraph. The production crew of Bon Cop, Bad Cop also had to use fake names for the provincial police services that it's respective protagonists initially hailed from for legal reasons. Yes, the OPP and SQ have IP lawyers on call.

Related note: Geoffrey Mandel mentioned years ago about having to create graphic design stuff for Peruvian army personnel stuff for an episode of Agents of SHIELD for similar reasons.