I have no idea. It's just a theory, and here's my logic: I can only think of two aspects of networking (other than the fragmenting process itself) that should be significantly affected by MTU: jumbo frame support and path MTU discovery.
I'd be surprised if path MTU discovery were at fault, because lots of Mountain Lion users go to YouTube regularly, and I don't see everyone screaming about this. So unless your local router is so utterly broken that it always refuses to pass along any packets marked "do not fragment", I wouldn't expect it to be the culprit.
If you want to check to see if path MTU is likely to encounter problematic behavior, though, you might try using ping with the -D flag to set the "Don't fragment" bit. If you get a lot of packets that bounce back (e.g. ping: sendto: Message too long) even with fairly small ping sizes (use the -s flag to set the size), then some part of your route is doing something naughty. :-)
Either way, it's a really bizarre behavior. Jumbo packets seems like a possibility because switches that don't support jumbo frames typically drop them entirely, so a single non-jumbo-frame-capable switch between two fully jumbo-frame-capable devices could potentially cause serious headaches, or at least historically did. Not sure about how that is handled by modern OSes.