I was on a consultant-assignment at a company that got raided by the police in the EU. The police was extremely careful not to scan any data that where stored on US-servers. The company used Google for mail and file storage, so all computers had to be taken offline before they could scan them.
While I don't doubt they have a way of getting permission to access that data, I don't think they will put in the effort unless you're a relally big fish.
Maybe he wanted to make sure a lot of copies of the evidence were floating around. Surveillance capitalism is like a free unlimited backup service you can't restore from.
He describe himself as an anarcho capitalist so I guess, ideologically, it is government surveillance that he is concerned with and that the free market will sort out the rest.
How did he get the videos out of the cameras that were seized if the recording was also not uploaded? Can Nest cameras upload/stream to private servers? (never had one so I have no idea)
While I don't doubt they have a way of getting permission to access that data, I don't think they will put in the effort unless you're a relally big fish.