I haven't seen anyone ask what level of control this apparently theoretical SDK will have. These are two entirely separate matters. The SDK AMD will release will be made and controlled by AMD, there is as yet no question of this, I've seen no one question it. Later on at some stage AMD may choose to pass this off to a third party to control, if they do or not we won't know till they do it. We have every reason to believe they will based off a history of doing such things that hurt them but help the industry(gddr of many types, lots of other small things that end up in DX, HSA).
In terms of who it gets handed off to, it doesn't have to be EA/Dice OR Khronos, OR MS, but no other options.
Historically when something like the HSA foundation gets passed off companies nominate someone internally to be their voice in such a foundation. Sometimes these people would say stay AMD employee, have lots of other responsibilities at the company and the foundation and being their spokes person for it is just part of their job. Sometimes someone will leave said company for a foundation but have their best interests in mind. Sometimes groups of companies will nominate/vote for who gets to be on the board/control. There are loads of ways it could be sorted out and speculating now is frankly silly. The most likely situation is that Khronos is FAR too problematic to get them to add Mantle to what they control. I would say most likely a new group with some AMD, some Nvidia, some Intel(and I suspect they would be a less interested, involved but less interested) guys, some industry guys, some big names, maybe a Carmack, or Gabe, both, neither.
It's basically silly to speculate. By the time Mantle is ready, there may be a better solution, Nvidia may talk to AMD/Intel/some game dev's and say they want a new API , akin to openGL control structure but they refuse it to be Mantle, and a group start something new from the ground up.
They'll release a public SDK, because it's insane not to. They've said they will, the dev's involve expect them to and fundamentally, it's illogical to prevent more dev's being involved. If the end goal was to refuse to bring dev's on board, then every penny being spent on Mantle is a complete waste.
As and when FUTURE SDK releases happen, and under whose control is questionable. When these things happen such api's would usually be pushed into a working state before being handed off. expect a beta sdk, then a final sdk(their early tentative dates were around april/november for beta/final, which I would expect 2-3 months later on each), then IF it gets handed off, expect it to happen sometime after a final SDK is released.