Absolutely. It would be completely in AMD's right to do that. And it would be up to the developer to decide whether or not it was acceptable to use that mode or not. Just like it was up to developers to use Mantle or not, something that wasn't available to Nvidia.
However, in your hypothetical case, within a week, Nvidia would release a driver that patched the shader to used FP32 instead of FP64, instead of just whining about not getting access to the source code.
(Every time this kind of topic comes up, it fills me with incredible joy that AMD chose to 'sabotage' Nvidia with Tomb Raider and TressFX. And that Nvidia was able to fix it within a week. It's a gift that will keep on giving.
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