Good point about comic genius, Guy. A lot of old shows succeeded because of great casting. E.g., Don Adams in Get Smart or Elizabeth Montgomery in Bewitched. The shows were not incredibly well-written or funny, but the actors made them work.
I'm not sure anybody thinks F Troop was a success. But if they do, it's probably because of Larry Storch. If the show hadn't had him, it would've been even more forgettable than it was.
Casting the Hekawis
But I disagree with your other point. I doubt F Troop's creators used Italian actors as some sort of ironic commentary on Hollywood's casting policies. I suspect they were following the common hiring practices of the times.
You can spoof cowboy-Indian relations with real Indians, you know. It's not particularly hard to do. See Little Big Man or Buffalo Bill and the Indians, for example.
If the F Troop movie uses fake Indians, it'll be spoofing the Indians themselves, not their relationships with the Army. I suspect Natives will protest that vociferously. It'll probably make the movie an epic failure before it even premieres.
For more on the subject, see The Best Indian Movies.