Yeah. My point is this "There's a 1 in 1024 chance of this measurement being a statistical coincidence." I understand this as "There is a 1:1024 chance that a statistical coincidence is the cause of this result".

But that's wrong, the statement must be: If it is a statistical coincidence, it had a probability of 1:1024 of occurring. But then the probability that it was cause by a statistical fluctuation is 100% -- It's assumed to be true.