I've always just turned the net over on the bottom side, and it hasn't caused any discernable problems for me. I haven't tried laying directly on the netting, but I don't see how it would hurt anything, as long as you didn't rip it somehow (sharp object in pocket, etc).
“I think that when the lies are all told and forgot the truth will be there yet. It dont move about from place to place and it dont change from time to time. You cant corrupt it any more than you can salt salt.” - Cormac McCarthy