What about the 300th request? I guess it's a matter of opinion, but is it better to provide a mediocre (or worse) quality experience to all 300 users, or to provide a good quality experience to 1/3 of the users and deny the other 2/3 requests?
On the other hand, you have Monopoly Street View, which launched with a massively higher number of players than they expected. The end result was a game that was playable for a very, very small group of people, and no one else even knew what was going on.
In general, you need to be able to balance the two. There should be a point where you have an absolute cutoff, no more users/requests beyond that, but you should also have a sliding scale. Of course a server only processing one request at a time will be faster, but you need to be able to degrade somewhat, while still providing good service.