Basically the reason was Minnesota was willing to give him their full MLE, so the Kings offered more to retain his services. Interestingly, while Hayes was gone in Sactown, they ended their huddles with "Chuck".
Why is this a classy move? They messed up his diagnosis. You don't go from "you can't play bball because of an abnormality" to "hey you're cleared to play". Obviously their doctors ****ed up, and the $1.3M is settlement money so Hayes doesn't take them to cleaners for emotional distress. Think about it, Hayes was a FA and they voided his contract and leaked his medical condition to the public without getting a 2nd opinion first. If Hayes didn't get a 2nd opinion on his own he'd be without a job, no money and he'd think he can't do any athletic ability for the rest of his life because he might drop dead at any second.
1) First and foremost Chuck deserves every penny of the new contract. 2) The Kings screwed up the first time. It's like going to a restaurant and they screw up your order and so they comp you with a free drink or dessert.
They voided his contract before a second opinion because they only had 6 days to void it or they were stuck with it. I'm sure they told Chuck beforehand that if the 2nd opinion cleared him they wanted him back. In this case, the Kings have done the right thing for themselves and for Chuck.
This... the bump in the price was to ensure he resigned with them and didn't hold out to get more with someone else. Namely the Wolves as stated above.
Mickey Angelo's scenario makes the most sense. Repped +1. It reminds me of the scenario with 10 day contracts. Morey would waive the player after 10-day contracts to get more time to evaluate. The player must be signed for the rest of the season after some point. It would leave Morey stuck with a permanent contract on a player.