To clarify this, the government has to go through certain procedures to seize your private property. If you own a hardware server, it is your property, even if it is sitting in someone else’s data center.

Supposedly they have to do that for safety deposit boxes too, but as recent events have shown in LA, that doesn't stop them from seizing everything including those boxes and then opening them up to take inventory. A judge objects, but it's too late. Now people are having to prove that they own whatever was in those boxes to get back their stuff back, and if they can't -- everything is gone.