I am usually asked to provide proof of certification to rent, to dive, and to get an air fill. Not when I want to buy. My spouse works in a dive shop. They ask for proof of certification for rentals and air fills (and to join in on shop-organized dives). Obviously they have some of this proof on file already if they have themselves certified the divers and they don't require the same diver to repeatedly show his certification. However, they do not have a policy to ask for c-cards for buying equipment. This is in part because people often buy equipment for others as gifts, and because it is both a small shop and the only dive shop in the city - they do know their customers and usually the people buying gifts for their customers well. The reality is also that people can go online and buy without showing c-cards, or yes, buy on ebay, kijiji, etc. Further, as someone in the legal field myself, the liability that can attach to a shop for renting gear versus selling gear can also be drastically different.
Personally, I feel quite alright with being asked for proof of certification, and would never feel comfortable owning a shop myself and not asking for it but I can see why some shops would opt out of it due to convenience without necessarily understanding the legal risks they may be taking. My spouse recently got a lot of pushback from a new customer who came in to rent gear without his c-card. He had called ahead (from near his home about an hour away) and had been told by another employee he needed to bring his c-card. Rather then turning back while he was still close to home and taking an extra few minutes to grab his c-card, he came in without it and was ticked my spouse refused to rent him gear without the c-card. At some point he revealed he had been certified many years ago but does not really dive. Anyway, while the shop can usually check certification through their own records or the agency, if it was too many years ago they might not be able to as was the case here (and this can vary with the agency). No one at the shop could remember this guy from 20 years ago since he obviously was not very active in the local dive community. He pleaded, became argumentative, and so on. Too bad, my spouse was not going to do it. The guy then drove all the way home and came back (with his c-card) and rented a tank and regulator. When he returned the gear, it was also pretty clear he had not treated it properly and it now requires overhauling. It is suspected he needed to get into his dugout on the farm and just plunked the tank in place in the mud in the bottom and breathed off of it. He is now on the "do not rent to" list. Point here being is that there are many shops that would have rented the gear and not potentially lost the customer by making him drive another 2 hours to pick up his c-card. Many shops, or specifically employees, might not want to deal with a customer pushing back on the issue and just decide to "risk it". Personally, a customer who does not see why there is a need to check certification is not one I would care to have anyway. It is not just for the shop's benefit that certification is checked.
Obviously even with a c-card there is no guarantee the renter will be competent or be using the equipment in a safe (or appropriate) way. However, at least the shop can assure themselves that the person has been trained at some point and do their best to shift liability in the event something did go wrong (like if the guy had ran out of air in his dugout).
Personally, I feel quite alright with being asked for proof of certification, and would never feel comfortable owning a shop myself and not asking for it but I can see why some shops would opt out of it due to convenience without necessarily understanding the legal risks they may be taking. My spouse recently got a lot of pushback from a new customer who came in to rent gear without his c-card. He had called ahead (from near his home about an hour away) and had been told by another employee he needed to bring his c-card. Rather then turning back while he was still close to home and taking an extra few minutes to grab his c-card, he came in without it and was ticked my spouse refused to rent him gear without the c-card. At some point he revealed he had been certified many years ago but does not really dive. Anyway, while the shop can usually check certification through their own records or the agency, if it was too many years ago they might not be able to as was the case here (and this can vary with the agency). No one at the shop could remember this guy from 20 years ago since he obviously was not very active in the local dive community. He pleaded, became argumentative, and so on. Too bad, my spouse was not going to do it. The guy then drove all the way home and came back (with his c-card) and rented a tank and regulator. When he returned the gear, it was also pretty clear he had not treated it properly and it now requires overhauling. It is suspected he needed to get into his dugout on the farm and just plunked the tank in place in the mud in the bottom and breathed off of it. He is now on the "do not rent to" list. Point here being is that there are many shops that would have rented the gear and not potentially lost the customer by making him drive another 2 hours to pick up his c-card. Many shops, or specifically employees, might not want to deal with a customer pushing back on the issue and just decide to "risk it". Personally, a customer who does not see why there is a need to check certification is not one I would care to have anyway. It is not just for the shop's benefit that certification is checked.
Obviously even with a c-card there is no guarantee the renter will be competent or be using the equipment in a safe (or appropriate) way. However, at least the shop can assure themselves that the person has been trained at some point and do their best to shift liability in the event something did go wrong (like if the guy had ran out of air in his dugout).