The woman who made the video knows the target and he may even live at her address. She has, based on what she says, some eccentric political beliefs. "You have been served" and other statements sound familiar but I would not want to try and identify the movement.
I also believe she expected the knock on the door because the video camera was at the ready even before the first sound. Even though I use my cameras a lot, I would be hunting for the zipper to the camera bag and maybe a blank tape way too long to be effective.
The target of the search may even have been there and fled just in time.
On the other hand, everyone knew they were being video taped. It would not have compromised anything for law enforcement to have interacted with her first and been very polite, asking if she knew where the target was and asking if one, just one, of them could come in and prove to themselves he wasn't there.
Instead, they acted like arrogant thugs. Perhaps they knew this woman and were tired of her bs over many weeks or months. But still, they knew they were on camera. The whole situation would have been different for the viewer if they said "please" and "thank you." The fact that they didn't makes me even more suspicious of their character.
Now, because of their behavior, they are being investigated and their department has a public relations problem that may cause them problems with other residents. They may have been in the right, but somehow I doubt it.
I would say you have given and excellent appraisal of the situation.