Actually, depending on how you want to imply it, "false positive" could mean a lot of things. In this case I meant that the badges could be tripped when no actual theat was there. (yes, there HAD to be a change for the badge to register, but that cause was not a threat)
Also remember (if I read it right) that your "badge" is responding to mana in the trigger, thus a dual natured critter could set it off as well. And so could awakened plants and the like.
With that in mind, I think it would work great in low magic facilities where there is a low chance of running into paracritters, mages, or parafauna. But in a high magic area, or in a Corp with a high number of awakened employees, paracritters and magical plants, your chances of a "false positive" goes up.
I.E: Sam the Mage walks too close to Sally the receptionist at the water cooler with an active foci. Or Mary the flower lover sniffing the awakened roses. Or even Nugget the cerebus hound giving acidic kisses to Paul the gardener. All these things the badge could pick up (again if it came within 4 inches of the badge) and are all examples of a "false positive"
Also, it's only half the system. The other half is the protocol that comes in when an alarm is tripped. This could be anything from a phone call to that employee so he can answer a challenge, to full mobilization of a heavy security team.... And this is where companies can fall down.
If everytime an alert is sounded the building goes on lock down and a HTR team is mobilized... All for a "false positive" (fuckin Jack cuddling the hellhounds...AGAIN!!!) then things get expensive fast (mainly through lost productivity) not to mention stressed out employees.
However, if the protocol is a simple call to the commlink of the tripped employee with a challenge (today's passcode please Tim... And stop smelling the awakened tulips!) then it could be alright.
Again, it think it's a great idea for low magic corps/facilities.