Once they use em folks will know. They will use em to prove they were right. They will not be able to then claim they didn't record the other stuff.
Sure they will. People leave stuff at home or forget to turn it on all the time. Some of my least favorite security incidents involved at least one of the unmonitored cameras or recorders turning out to have a dead battery or no memory card (or a full one) by the time the incident started, and there have been at least a dozen times I only remembered to turn my windshield mounted GoPro on after something already happened that I wish I'd gotten on camera.
And that doesn't even count incidents of recording something, deleting it and pretending it never happened.
Hell, swap the cards daily, and keep yesterday's handy; anything happens, switch to yesterday's card, ditch today's, and let anybody try to prove you didn't forget to turn the camera on, or fail to notice the card was already full.