37Signals would see significant savings in development and maintenance costs -- and increased customer satisfaction -- if they approached this staffing requirement as a band-aid, not as a final solution, and took a long, considered look at the root cause of this systemic failure.
While I certainly have to think that 37signals knows what they are doing, the need for a 24/7 programmer does sound a little strange. Perhaps it's just a question of semantics, as the post describes dev/ops duties more than anything else.
An actual need to do programming instantly and with no warning is quite a different proposition, not one that I'm aware of having ever been needed in any of the companies I've worked for.
"We spend time trying to figure out why emails weren’t delivered (often because they get caught in the client’s spam filter or their inbox is over capacity), or why an import of contacts from Excel is broken (because some formatting isn’t right), or any of the myriad of other issues that arises from having variable input and output from an application that’s been used by millions of people."
An absolute majority of these issues were caused by bad system architecture issues (which, to be fair, in financial company is usually not up to the technical people to solve).
And also, today a much better solution is available: instead of requiring people to be on call at nighttime, why not hire people in different time zones, across the world, specifically for the purpose of Level 2 support when your main devs are asleep?
Most problems of this sort are not very serious -- if you've got serious problems all night then that's a systemic organizational failure)