Don't know who compiled that list - some of those dogs breeds are notorious for triggering allergies! As a general rule of thumb, allergy sufferers seem to react more strongly to the smooth coated and short coated breeds, so I would try to rule all of those out.
There are not many breeds on the non-shedding list that I would actually recommend for first time dog owners. But I know several people with severe allergies that keep shedding breeds, they are just scrupulous with washing their hands afterwards or some just take an anti-histamine every day. Maybe your GF could try visiting relatives with dogs and see how hard it would be to manage her allergies.
If you don't mind being on a fairly long waiting list, you could try a Bedlington Terrier. They look like a small greyhound with a curly coat and have wool, not hair, like a poodle. Although they can be a stubborn breed.
You can clip a poodle so that it doesn't look poodly, combed out they look something like Benji the dog movie star. You can do the same with a miniature schnauzer, they have a wider muzzle than the poodle if you prefer that look. Don't get a standard or giant schnauzer they are guarding breeds and not very suitable for first time dog owners.