I believe there are a few exact draws, yes, and what happens is that the medal does get shared. A draw in third place leads to that event awarding a gold, a silver and two bronzes; a draw in second place leads to two silvers and (I think) no bronze. In fact, apparently each of those happened once this year. I don't think there was a draw in first place at any point, but it seems clear that there'd be two golds and a bronze awarded if there were. (Or there might be emergency sudden-death playoffs of some sort, but if those failed then that'd be the obvious fallback position.)
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I believe there are a few exact draws, yes, and what happens is that the medal does get shared. A draw in third place leads to that event awarding a gold, a silver and two bronzes; a draw in second place leads to two silvers and (I think) no bronze. In fact, apparently each of those happened once this year. I don't think there was a draw in first place at any point, but it seems clear that there'd be two golds and a bronze awarded if there were. (Or there might be emergency sudden-death playoffs of some sort, but if those failed then that'd be the obvious fallback position.)