I did some scouting around about how addition reactions involving a cyclic intermediate can lead to Markovnikov products (products that you would predict would form from Markovnikov's rule, based on a carbocation intermediate). The explanation as I understand it goes like this:
Fact: cyclic alkenes that undergo addition of halogens like Br2 end up with the halogen atoms trans in the product. Similarly halohydrin formation results in trans configurations.
Fact: a carbocation mechanism does not agree with the statement above, so it does not explain the reaction.
Fact: cyclic intermediates such as the bromonium ion can be appealed to, and provide an adequate explanation for the trans stereochemistry. So we use this mechanism.
Fact: these reactions yield Markovnikov products.
It's these last two facts that seem contradictory, unless you take a more nuanced view of the cyclic intermediates. Imagine that these intermediates are not exactly symmetrical. If they are shifted a bit so that there is some carbocation character in the cyclic intermediate, then we could explain both the trans orientation of the added groups and also the Markovnikov product formation. Which is the best explanation there is.