That's what I thought, but appparently not. As mentioned in other posts, the stuff in pool bromination tablets is trichloroisocyanuric acid, except one of the chlorines is a bromine. This is a good, clean chlorinating agent. In the pool bromine package, there is also NaBr. I suppose the idea is that NaBr + Cl ion -> NaCl + Br
I don't think chlorine would take bromine over sodium, somehow...
Remember, however complicated the molecule may seem, it has to release its chlorines or bromines into the pool water, so they can kill the nasties in there.