I believe if there is a huge win on the line, they have an account so there should be money putting on that account when they won something, instead of claiming on chat. Sure that is another way of doing it to make people stay online and chatting, they could claim that way if they want to, but at the same time I feel like there is a huge chance that the person who bets on the 5.8 million may not be able to chat at the same time and be too late to realize he hit it and chat.
So, I suggest if a person does it, we all know their account, just put the reward on their account and notify them with the mail they registered and that's it, we do not need them to be on chat. This would cause the chat to slow down a bit but it would also make sure the winner gets it for sure.
Given that the bounty is provided by the site, it's fair for the site to decide how to set up the rules for said bounty.
There are valid arguments for doing it the way you propose, but there are just as many (if not more convincing) arguments to do it the way it is right now.
However, the thing that is discussed here is not a change of the bounty rules, but semantics about the "real winner" with the current rules in place.
And after all, Shahista won it, claimed it, and everything said before about there being "no real winner" was pointless anyway.