Actually, he took a demotion. In the 50s show he had been promoted to lieutenant, at some point. When he revived the show, he figured that since he was doing a “procedural” it looked sort of silly to have a lieutenant go around knocking on doors, so he bumped himself back to sergeant.
As to the OP, it is plausible. The 50s show was created in an era when everyone simply assumed that the cops were the good guys. (I saw a movie made from the 50s series, once, in which he wandered around violating suspects’ civil rights and breaking all sorts of department policies.)
In the 60s, there was an upsurge of anti-police feeling against which his show militantly tried to provide pro-police propaganda. It is quite possible that eliminating the word “cop” (which has never been an insult, but has been considered less than respectful), was part of that mission.
On the other hand, however plausible it seems, I have never seen that put forth as fact.