"You are allowed to record stuff happening in private spaces depending on the situation and state you are in."

The part about "depending on the situation and state you are in." is doing _a_lot_ of work there. Here in WA state, for example, if you go into a private meeting and record the thing without getting folks consent first then you're guilty of a misdemeanor.

Another example: in my old neighbor we had a nuisance neighbor who we all thought was engaged in Crimes, Plural. The immediate neighbor wanted to put up a video camera to catch them in the act but was told that they can't film the neighbor's yard directly. Filming their own yard and the field of view happens to catch something in the adjacent yard might get by a judge, maybe. So even if you can stand on the sidewalk and see past the trees into someone's backyard that doesn't mean you can film it.

(To be clear - I think this probably a good rule. I don't want folks filming me in my backyard :) )

Clearly, the tl;dr is that if this really matters to someone then they should check with a lawyer first.