Brazilian leftists in general do have a history of radical opposition to the military police. Some radical left parties propose abolishing it outright. "The military police has got to end" is even a line in at least one leftist movie, uttered by a "fascist" police officer no less. It's definitely an idea in the memespace of the Brazilian left.

So in my opinion this "gaffe" is just him revealing his true colors in public. Like when someone gets drunk and starts saying what they're really thinking.

There were numerous fact checking services, none of them particularly trustworthy. The "official" fact checking came from Globo, which hosted the debate. They're known to be biased towards him. They literally helped him out during the debate when he started screwing up his time management.

I had Astra perform a thorough fact checking on both debates, and the fact checking of Globo and other major newspapers. It found a certain degree of favoritism towards Lula.