Google / YouTube needs to send traffic AROUND problems instead of through them.
Notice, that getting to YouTube isn't the problem, it's how YouTube sends it back.
This is why the OpenDNS trick works, because it forces Google / YouTube to route you differently.
Getting on the Internet was the responsibility of Qwest, however sending something back isn't Qwest's problem.
Here's an analogy to the problem :
You can write a letter and put it in your mailbox very promptly but if the addressee has a problem, somehow it's the local post office fault and not the remote one, even though we know the remote office has problems (look at the trace route)