Been reading through the above comments as I have one of the circular "folding" landing mats. I can quite understand how all of the problems arise.
My mat has 4 fabric loops and was provided with four plastic pegs with which to peg it down. I don't often use them as the mat is fairly stable at ground level on smooth, level ground, but now I'm contemplating removing the metal ring and always using the pegs to stabilise the mat.
As long as you aren't calibrating the compass near the ring it's not a problem. I've been using one for two years? now without any problems with my Inspire 1 and my FireFly 6.