From what I understood, the parent's question is not about Microsoft updating grub; it's about a person hit by the bug, and thus in a situation where Windows boots but Linux doesn't, using Windows to copy the correct file (probably extracted from an updated package from the Linux distribution they're using) to the correct place in the EFI partition by hand.

(The first obstacle would be that AFAIK the EFI isn't mounted by default on Windows, but I believe it should not be hard to tell Windows to mount it and give it a drive letter.)

Why? You could just copy the binary and signature to your EFI partition from Windows? What am I missing here?

MS could just sign it with whatever three-letter agency certificate they usually cooperate with. /s