If my landlord's unattended lawnbot runs over the mailbox and destroys a video that my friend sent me, he's going to be held responsible, right?
Property rights aren't absolute. They just aren't, sorry.
In general you can't damage someone else just because they happen to be on your property. Not tenants, not guests, and in some cases, not even trespassers.
Your landlord can't, because the video is your property. A copy on Google's servers isn't, even if you retain the copyright.
In any case, none of these are proper analogies. Google is providing you with a service, not holding stuff for you, and they're simply cutting people who have no contract with them except for their own ToS off.
Isn't it a bit of a stretch to suggest that Youtube taking down videos is damaging to the owner?
I see the analogy more like this -- if you place your mailbox on my property (your video on youtube), the unattended lawnbot moves the mailbox off their property.
