That's very interesting. I see your argument. I haven't seen a treatment of acidity like that before. Perhaps my entropy argument is flawed!
Unfortunately, my skills at thermodynamics are lacking and I'm not sure how to compare the two compounds in question with any certainty. The URL you showed certainly suggests that the change in entropy for converting the bromohydrin to the acid would have a negative entropy (induce a more ordered system) but I don't know how to account for changing from an alcohol to a ketone. I would think that removing the possibility of hydroxyl hydrogen bonding would allow for a less ordered system (positive entropy), but I don't know for sure. Moreover, I don't know how the magnitudes of these effects would compare.
Thanks for that link, it was very interesting to read. By the way, did you happen to work out all of the bond energetics? I'm curious to see how they compare.