It's ridiculous if taken literally as a universal prior or bound, because it's very easy to contrive situations in which refusing to give probabilities below 1/10^12 lets you be dutch-booked or otherwise screw up - for example, log2(10^12) is 40, so if I flip a fair coin 50 times, say, and ask you to bet on every possible sequence.... (Or simply consider how many operations your CPU does every minute, and consider being asked "what are the odds your CPU will screw up an operation this minute?" You would be in the strange situation of believing that your computer is doomed even as it continues to run fine.)

But it's much more reasonable if you consider it as applying only to high-level theories or conclusions of long arguments which have not been highly mechanized; I discuss this in http://www.gwern.net/The%20Existential%20Risk%20of%20Mathematical%20Error and see particularly the link to "Probing the Improbable".