If my landlord's unattended lawnbot runs over my kid, he's probably going to be held responsible, right?
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.
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.
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.