Here’s what bothers me about the situation. You remove the video, no problem. Someone else may have downloaded the video and re-posts it. Do you think management will believe you are innocent?
I agree with scratch, let the picture taking and video work stay in the hands of management. Yes, I have a cell phone camera, and yes I have used it at work. If I snap a picture while on the clock you can bet my sup will be looking at the shot. The shot will also be in some way a benefit to UPS. You don’t (I hope) walk into a neighbor’s house and start taking pictures without permission, why do it at work?