Stumbled upon this on my last playthrough and figured out might help a few people.
You know how when you encounter something in the game for the first time, a little prompt for its Guide entry appears, in the same way as pocket secretaries and story items? The alarm system is one of them; the prompt only appears if you trigger an alarm. I don't recall seeing the prompt on my first playthrough, in which I didn't get FotH, but I saw it in the Guide list (though the significance was a fridge moment)
TL;DR - Check the guide section in the menu; if "Alarm System" is in the list, you've failed Foxiest.