Easy: If the cops tell me water is wet I trust them. If they tell me to not trust my own eyes when they do something wrong I don't.
Cops in the US operate under perverse incentives. Knowing these incentives will help you to decide when you can consider trusting their statements and when you can not.
It's not something you really need to keep track of. The recommended approach is to use your brain and consider all of the context available to you on a case by case basis. But I suspect this is more about not wanting to accept the ever increasing evidence that Elon's characterization of what happened was largely a farce.
when they stand to gain / justify bloated budgets, they are probably lying. when they have nothing to gain, and contradict the worlds least reliable source, they are probably not lying.
Perhaps that's good. This could be an opportunity to engage your own critical thinking and rather than just blindly trusting or distrusting anyone you evaluate the facts for yourself.
Nobody was willing to sign their name to a report saying any member of Elon's family encountered a stalker. Reporters, who were then banned from Twitter, had already determined the time of the video was not close to any flights, nor was the location close to an airport.
Cops in the US operate under perverse incentives. Knowing these incentives will help you to decide when you can consider trusting their statements and when you can not.