There are three concepts involved: an evidence "e", for example "I extracted 1 black ball"; a hypothesis "h", for example "the urn does not contain only white balls"; a theory "h <- e" that, by means of logic or otherwise, deduces the hypothesis from the evidence. Your (qsort) theory is that if you see a black ball then the hypothesis is correct.
Everybody, including you, me, and Deutsch, agree that if the probability of the evidence goes up, then the probability of the hypothesis goes up as well.
What Deutsch and Popper/Miller are also saying, however, is that if the probability of the evidence goes up then the probability of the theory goes down (proof in the paper).
I need to study the paper more carefully, because I am not 100% sure that it is strictly correct (there are many factors that would transform a < into <= if they were 1, and I suspect that some are), but I believe the weaker statement that if the evidence goes up the probability of the theory does not go up at all.
In any case, this conclusion is consistent with what all scientists have believed forever: the only way to increase confidence in a theory is to try to break it. Or at least they believed this until fact checkers and censorship came along and threw the baby away with the bathwater.