I've never been turned down, but many PADI shops didn't recognize my original Los Angeles County c-card from the 60s and requested a check-out dive before I did any other dives. Too bad these PADI instructors didn't have a better understanding of the history of this activity and knowledge of the far more rigorous LAC certification programs. I finally met a PADI instructor in Cairns, Australia, who not only recognized my c-card, he referred to it as a "museum piece." I asked about getting a PADI AOW card from him and he was very helpful. I'm not bashing PADI here... the same thing might have happened had I dived with a shop associated with other agencies.
I also think of a story Bob Meistrell of Body Glove/Dive N Surf told me about a dive trip to the Philippines back in the early 60s. He had forgotten his c-card and was told he couldn't dive. The group vouched for him and when the local divemaster saw Bob underwater he said no need to find the card. For those who don't know, Bob was one of the very early Los Angeles County instructors and a legend.
By the way, I keep scanned copies of my c-cards on my web site with my dive log so if I happen to forget my c-card, I can point the shop to my web site to verify my certification.