True or not true, I don't really care, but I carry the cert for the firearm I have with me at the time, restricted or non restricted. My time is important to me, and I don't need it wasted waiting around for someone to verify if the firearms I have are mine or not. All my certs are laminated, are paper thin and I see no issue in putting them in my wallet, backpack, pant pocket, ammo can, and so on. If I get asked, I can produce the documents required and I am on my way within minutes, and I can enjoy my hunt, my target shoot, or even the drive to the activity or just getting home. I don't find it a burden to have the right documents with me, fortunately so far I have never been asked for them.
To me it's the same as having my drivers license, ownership, insurance, credit card, debit card, one never knows when one will need anyone of those, but being without them can only cause time loss if you don't have em with you and you need em......
Just to clarify, I only have my certs, att and any relevant paper work for my firearms only during the times I actually have firearms with me, the only 2 things I carry always that are firearm related are my RPAL and Outdoor Card