This is factually incorrect. When I press a globally grabbed key, it goes only to the grabbing application. It wouldn't make sense for the windowing system to deliver a single input event twice.
I feel frustrated and annoyed when you focus on issues that are only tangentially related to the subject of threads because it has the potential to make others uninterested or unwilling to participate in on-topic discussion.
This
https://my.mixtape.moe/xgmeiw.flv is a video showing exactly what I'm talking about. VLC has keyboard and mouse focus and I am pressing the Play/Pause button on my keyboard.
Here is a GIF of a section of that video:
Again, this is only tangentially related. It is context. Is not the question or problem.