If I create a lawn-mowing bot that goes rogue and runs over the neighbor's cat (or in a less-bloodthirsty scenario, wrecks his expensive landscaping) I'll be held responsible, yes?
I don't see why automation should be an excuse. If anything, systems that are intended to operate without human supervision should be held to a greater standard of safety, not a lower one.
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.
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.
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.
Google has chosen to make money from other people's content, and as such they have a responsibility to treat that content with respect.