It does, actually. This combined with a problem I was having with the Dropbox desktop app is starting to paint a slightly clearer picture of things for me. I used to live in MN for a few years and I had Comcast there, and I used my own router. Whenever I put a large file in my Dropbox folder, it would sync, no problem.
Since I moved back to MD, I have FiOS again, using their older G Actiontec router (from the sound of it, you have a newer model.) Now if I put a large file in the Dropbox folder, it brings the whole network to its knees, not just my computer. Both inbound and outbound connections are choked. If I restart the router and stop/start DB syncing, sometimes it'll behave itself again, other times it will only last for a few seconds before flaking out again.
I think the issue may be with the router's inability to properly schedule large numbers of outbound packets. The router freaks out, and a backlog of waiting packets builds up until it all boils over. Since TCP/IP requires an acknowledgement packet to be sent when one is received, that means downstream connections that are expecting responses won't get them (because of the backlog) and will attempt to re-transmit their packets and will eventually timeout or reset the connection as being unreachable.
If iTunes was too aggressive in sending its return packets for multiple simultaneous downloads, it could have been overwhleming my router, just like Dropbox was (is). It's just a hypothesis, but it fits the facts. When I have some time (and money) I'll try replacing my FiOS router temporarily to see if that resolves the issue with both applications.