The key is that the salt speeds up the heat transfer of the ice to the can. I do the salt/ice trick, but I’m also happy drinking a warm beer while the rest of them chill down.
No, salt does no such thing.
Salt melts ice at a lower temperature than fresh water - so salt water can be liquid well below zero C (below 32F)
Obviously, the colder the bath, the faster the heat transfer out of the can/bottle. Heat transfer is roughly proportional to the difference in temperature.
Fahrenheit invented his scale by mixing salt and ice to come up with the coldest temperature achievable by any experimenter in a lab (at the time). He called that 0F.
Salt melting ice - ice requires additional calories to melt (heat of fusion) that heat comes from reducing the temperature of the water, thus chilling the water below fresh water freezing.