Few people want to do a site wide search and the ones who do will press the input box on the top left. No one expects that ctrl-f will open a site wide search, everyone expects a page search.
If you still want to enable this ctrl-f to enable the site wide search, I suggest making it opt in with the checkbox. It's really obnoxious to have to disable the checkbox.
If regular users find it helpful, maybe advertise this as an opt-in feature?
To be honest, the non-standard behaviour plus strange looking popup confused me. I didn't even notice the tiny checkbox, nor that you could press CTRL+F again to get the standard search behaviour. My mistake, of course, but this speaks of poor UX in my opinion...
If you still want to enable this ctrl-f to enable the site wide search, I suggest making it opt in with the checkbox. It's really obnoxious to have to disable the checkbox.