As a groomer, I tell my clients all of the time the importance of a proper bath. Many people say they can bathe their dogs at home, which for some breeds it is fine - but others will benefit from going to a groomer. We are able to thoroughly wash the hair clean, completely dry the dog, AND blow out all of the undercoat, especially on double coat and short coats like Akitas, huskies, labs, etc. We can also see what is going on at the skin level to report to the client if we notice anything odd. Some owners can buy the force dryer and do it at their home, but most complain they don't want the hair everywhere. And if you have ever forced dried a double coat like a Husky, Keeshond, or Collie - you know the "snow" that happens.
Drop coats like Havanese, shih tzus, maltese dry very quickly even under a fan, so drying them like that is okay. I will use a box fan with no heat to dry some dogs who are very fearful of the dryer, especially on the head. However, even after drying with the fan, I always finish with the force dryer to make sure everything is completely dry. If the environment is very humid, it will take longer to dry, even with a force dryer. I'm in Houston - I have a dehumidifer in my salon and when I turn it on in the morning, it's at 95% humidity! I have noticed a huge difference in using a dehumidifier.
I wonder if the dog in the video had packed undercoat when he was bathed. Packed undercoat traps moisture and never allows the skin to dry. It is similar to heavily matted dogs where mildew and bacteria can grow at the skin level. Notice how the area that was affected is the neck area - a heavily coated area and also one where there is increased friction due to wearing a collar. This can cause matting and packed undercoat. Another thing - if there is packed undercoat, perhaps the shampoo was not rinsed out all of the way? Shampoo left on the coat will cause itchy skin and flaking. Maybe even an allergic reaction?