Since they probably have legal hip deep into patenting on the g-sync you can bet they will try to lock it down. Or extract fierce roaylaties. Look at PhysX that they effectively blocked if you tried to use both NVidia and amd at the same time. At the least, they will try to have either control or royalties taken from every monitor that will support it.
History is definitely on the side of your argument, but as PhysX was effectively blocked first from running on AMD hardware and then from being run on Nvidia hardware with AMD hardware as the renderer through software checks and exclusionary development, I think that superjawes does have a point. At worst, AMD/Intel would need to reverse engineer the signal that G-Sync hardware on monitors need and implement their own version of it, possibly risking a lawsuit in the process, assuming that Nvidia isn't open to cooperating in some fashion.
At the same time, I doubt that Nvidia will refuse to support FreeSync, though I expect that they'll call it something else. They'll no doubt tout G-Sync as superior, and it may very well be, but I expect that they would prefer the marketing advantage of being able to support all variable V-Sync implementations, something that AMD will be able to claim as quickly if at all.