Not really. They just extend the TWOV period rather than issue a visa. If the delay was going to be on the long side (like nearly a day or more), I'd go to the PSB at the airport to get whatever piece of chopped "permission slip" they'd be willing to give, to keep and show to Immigration. The reason I'd go to the airport office rather than an in-town office is that all the airline players are there to verify my story, and of course the PSB will need to verify.