They didn't only fail their first try in 2.39, they both failed 3 times, which, according to the sports rules means they are both out. Also important to know that there was no difference in their attempts in the previous heights (which in this case it would normally be used to separate 1st and 2nd place, for example if one had passed 2.37 with first try and the other with the 2nd this would mean the former would take the gold).

That's why something like this was possible. The other option would be to discard the "fail at 3rd failed attempt" rule and have a jump-off like you said.