Or, for instance in the case of particle physics, it means the probability you are just looking at background.
No, it's the probability that you'd see a result that extreme (or more extreme) conditioned on just looking at background. Frequentists can't evaluate unconditional probabilities, and 'probability that I see noise given that I see X' (if that's what you had in mind) is quite different from 'probability that I see X given that I see noise'.
(Incidentally, the fact that this kind of conflation is so common is one of the strongest arguments against defaulting to p-values.)
Keep in mind that he and other physicists do not generally consider "probability that it is noise, given an observation X" to even be a statement about the world (it's a statement about one's personal beliefs, after all, one's confidence in the engineering of an experimental apparatus, and so on and so forth), so they are perhaps conflating much less than it would appear under very literal reading. This is why I like the idea of using the word "plausibility" to describe beliefs, and "probability" to describe things such as the...
Another month has passed and here is a new rationality quotes thread. The usual rules are: