But I can see why the scriptwriter went for it - it provides as good a psychological explanation for the subsequent events as any. If Trenck did resemble Katte in whatever ways, it would indeed explain a lot..)

This seems to be a *thing* for people to do with Fritz. I've now seen three examples: the one you cite here, a documentary maker speculating that Catt was chosen for the similarity of his name to "Katte", and the playwright of "The Sorrows of Frederick" having Frederick decide that "freedom of conscience and penis" applies to soldiers who sodomize their horses only if said soldier is coincidentally named Fredersdorf (and "the" Fredersdorf is dead and Fritz misses him):

Frederick, after pardoning random Fredersdorf: What would have happened had his name been Schmidt?
General: He'd have been shot.
Frederick: I'm glad you have a logical mind.

I'm not convinced, myself, but okay, Trenck is probably the example that bothers me least, as far as fiction goes. (Personally, I just think Fritz was drawn to charismatic, quick-witted individuals: Katte, Trenck, Voltaire, Algarotti, Marwitz, Glosow, Keyserlingk, what seems like the entire Rheinsberg circle...)