Why is it every morning my perfectly dry bathmat it drenched? There is no plumbing problems. Has anyone else heard of this thing happening?

I don't know how your bathroom is set up. That will be key to understanding why that happens. We have a similar issue. We have a classic european drain-in-the-floor shower floor (it's actually not as horrible as it sounds), and I have noticed that if I leave a mat over it, it will sometimes get all wet even though no one has been using the water there. I figured out the problem. Occasionally water from the washing machine, dishwasher or sink (if there is a lot of water being used) will gurgle up a little from the drain in the floor. It's a problem with the pipes, and just enough water comes up to wet a bathmat well. If the mat is not there, the water disappears by itself. If you don't have this issue, it could be caused by changes in temperature, humidity or air pressure. I don't know why someone would haunt a bathmat. I'll bet if you move the bathmat it will stay dry...