This is a good point... the first step is getting ahold of the right person, but after that there will probably need to be some sort of dialog or coordination as the on-call person tries to gather more data about the issue, reproduce the problem, tests the fix, etc. Providing that sort of system would certainly be very useful for your customers.

Overall great idea with PagerDuty though, especially if one's business relies (survives) on their website's/system's uptime. Reducing MTBF is often very hard, especially after a certain point, and reducing MTTR is therefore very important for improving availability.