It's usually less of a bandwidth issue and more of a configuration problem - e.g. default Apache tries to spin up some 50 processes to handle requests, which can drive a small server into swap space.
In this case the 50 worker processes started by apache were just not enough to handle all requests. Each page hit creates about 30 requests for html,js,css,png and gif files, so each hit keeps quite a few workers busy. ;)
