Has there ever been an official source verifying this fact?
I don't believe there is an official source for any of this.
The closest I can find is this interview with Branagh. Quoting from it:
Certainly Branagh's most controversial bit of casting is having comic actor Micheal Keaton portray Dogberry, the officious constable who is just stupid and pompous enough to be dangerous. Employing a gravelly "Ahoy, Matey! " pirate voice and pretending to ride an invisible horse, Keaton's Dogberry seems guaranteed to blow the minds of purists.
"I've seen that part played so badly and so slowly on stage that it's put the play on the floor," Branagh said. "I wanted a brave, bold performance that would provide a surreal quality. And the vividness with which it's performed is exactly in the same spirit as the performances of Will Kemp, one of Shakespeare's great clowns, who was chucked out of the company for ad-libbing too much. I just know Kemp would have given a very physical performance.
"I figured Dogberry would be the hardest character to do for a modern audience. He's one of those dangerous, thick people who believe they are intelligent and responsible but are actually a few sandwiches short of a picnic. For example, the whole idea of having him ride in on an imaginary horse...We shot it several ways, including just having him walk and run, but this way was bigger and bolder.
"The truth - and I'll probably be struck by lightning for saying so - is that a lot of those Dogberry gags just aren't funny as written. The fun is in the size of the man's ego and his assurances about his own competence as a constable.
"I believe the closest thing to genuine Shakespeare in this century were the vaudevillians, who had to deal with rowdy audiences, a real cross section of people. Michael gave us a very dangerous and slightly bawdy performance, and I think it was absolutely right. "
So whether Branagh truly wanted this to be a tribute to Monty Python or not is unclear - instead, it seems he just wanted a completely surreal quality to the performance.
Python don't have exclusive rights on this style of surreal acting, so whilst parts of Keaton's performance are certainly Python-esque, that's because Monty Python as a whole is simply surreal and bizarre - which is exactly what Branagh had asked Keaton to do.