Let me propose a charitable interpretation of what brazil84 is saying (he can correct me if I am wrong). Here is an example:

We are discussing who committed a crime. There are three and only three suspects: Peter, Paul and Mary. Mary has an excellent alibi, so she's basically out of the running. There is some evidence both for Peter's and for Paul's guilt. Let's say we agree that the probabilities of each being guilty are: Mary 2%, Peter 49%, Paul 49%.

Then a witness comes up who saw someone wearing a dress in the scene of the crime. Since men are a priori unlikely to wear dresses, this lowers the probability of Peter or Paul doing it.. Let's say however that for whatever reason, we agree that it slightly less unlikely a priori that Peter would wear a dress than that Paul would wear it. Mary's alibi is so good that the new evidence only raises very slightly her probability of being guilty. The posterior probabilities are: Mary: 6%, Peter: 48%, Paul 46%.

This seems like a situation which might be described with brazil84's quote

"so situations can arise where evidence comes out which contradicts a hypothesis but still makes that hypothesis more likely to be correct"

in the sense that Peter's guilt, even though in the absolute sense less likely (the evidence "contradicted" it) should now be our top hypothesis; it is "more likely to be correct" compared to the only plausible alternative.

I agree that brazil84's way of putting it was a bit confusing, if this is what he meant.