That's the thing, there is no one rule that makes it all simple. The article, as some have pointed out, basically says there is not much science showing a cool down is beneficial to performance.
The most simple rule is to do basically what you think is right most of the time. What else can you do?
The cool down is always going to be a gray area, not black and white. If we look at something that is much more widely studied and understood, such as nutrition, there are still many gray areas. It would be hard to find several highly respected scientists, however, who said there is no scientific proof that proper nutrition benefits performance.
A question the article brought up for me was a question of PRIORITY. For example, where should the "cool down" rank on a semi-fluid list of post-workout priorities. For me, I have noticed that paying attention to proper nutrition (aka putting the right drugs (normal food and drink) in my body, at the right time) is incredibly, incredibly important. Definitely a higher priority in the long run than how many miles I run for a cool down.
So I finish a long tempo run that is both aerobic and anaerobic (to use a workout that challenges some previous posters' simplifications that you cool down after anaerobic but not aerobic). What should I do? Or, even better, what if I have 2 hours in which to do a workout, shower, eat and get ready for my next obligation (i think we can all agree that time constraints are extremely legitimate for many runners in western societies).
How do I use those 2 hours most effectively?
Option 1. warm-up for 30 minutes, 30 min tempo, 30 min cooldown, quick shower, meal, stretch and out the door.
Option 2. warm-up for 10 minutes, 55 minute tempo, 15 min "cool down" which is 5-7" jogging, 3" stretch and 5-7" laying with legs propped up to help with blood pooled in extremities. (that's 1'20"). Then immediately prepare a meal with lean protein, lots of fruits and vegetables and good fats like olive oils and nuts and appropriate water for the amount I used working out.
So in 1. I do a 30" cool down.
In 2. I do a 5-7" jog cool down but I also do more quality work, more threshold running, place more emphasis on eating properly... all in the same amount of time.
Why would so much emphasis be on the cool down when we can see that the cool down might be less important than things like nutrition, overall time spent running where the heart is beating faster and our nervous system is working at a useful level. Perhaps leg elevation, nutrition, an improved aerobic capacity are just more important?
I also have a rule that says "what do the Kenyans do?". The Kenyans cool down very easy (12" miles?) on a soft surface and then sip tea, eat healthy food and lay down. Hey, sounds like a cool down is good for them, but it's certainly not the only or even MOST important part of all the things that help them be ready to run again the next time.