My groomer has a really nice forced air dryer that gets them dry fast and they are so soft and their hair is straight. Just a guess, but maybe they mean drying it by hand with the forced air dryer as opposed to using a cage dryer? I wouldn't let them use a cage dryer.
I used my regular hair dryer until I bought a mini forced air dryer. I like the forced air because it's warm air not hot and my hair dryer has a tendency to over heat and shut off after 10 minutes or so and I always bathe them together. But yeah, unless you want to buy a $400 K9 forced air dryer, your regular hair dryer for 1 puppy is fine
Just keep brushing until the hair is completely dry. You'll learn through trial and error what brush works best.