Well you're going to be the genius here, because as it turns out, they're both wrong.
First, we're going to eliminate "novel" options for cooling, like liquid nitrogen and fire extinguishers, and limit ourselves to ways we can cool bottles every day in the freezer.
What we need to maximize here is thermal conductivity. Since the goal here is homeostasis, we need to move heat out of the bottle and into the surrounding medium as quickly as possible. And air, as it turns out, is a pretty lousy conductor. So that makes your first friend most wrong. Keeping the bottle dry will cool it eventually, but quite slowly. However, ice isn't that much better. Because there's a lot of air still touching the bottle when it's in ice. It'll cool it better, but it's certainly still not the best option.
The best option, it turns out, is an ice water mixture, with a healthy dose of salt to help keep the water liquid, even below 0 degrees Celsius. Water happens to be an excellent conductor, and with ice to keep it cold and salt to keep it liquid, can draw heat out of bottles faster than any other non-exotic method, by a significant margin.
So, if you want to cool your bottles quickly. and ice-water bath is the ticket.