I can't say that I've looked into it. The reason for this is because it doesn't make any sense to have a pinging service on the same connection as the one that you are trying to monitor. If the connection goes down, then you'd never know because the pinging service wouldn't be able to notify you.
The whole idea of a monitoring service is to have it situated externally so you can have it notify you as to when the outside world sees a problem with your site/server/connection.
How important is it to be using something like Pingdom for a live site?
It depends on how much you are concerned about uptime and downtime.
For my personal sites, I don't monitor them, as they don't get much traffic. For business sites, sure, I monitor them.