They don't need to purchase bandwidth, Youtube is available via public peering exchanges. The way these generally work is you just pay for the port on the switch at the exchange and traffic directly. See:
Purchasing a port on public peering fabric isn't the same as buying bandwidth from a transit provider. It's a great way to get traffic to your users much cheaper than you could via transit which is why people do it. The issue is eyeball networks - Comcast, FIOS, Time Warner etc. may choose not to do so because they went to seek rent in the form of "paid peering" from these same content providers that their users paid them to get access to in the first place.
https://www.peeringdb.com/asn/15169
Youtube is available via public peering at the Equinix Internet Exchange New York:
https://www.peeringdb.com/ix/12
Purchasing a port on public peering fabric isn't the same as buying bandwidth from a transit provider. It's a great way to get traffic to your users much cheaper than you could via transit which is why people do it. The issue is eyeball networks - Comcast, FIOS, Time Warner etc. may choose not to do so because they went to seek rent in the form of "paid peering" from these same content providers that their users paid them to get access to in the first place.