I have to admit I'm a bit offended by this article. I'm typically an avid fitness mag reader and I love a lot of their articles and success stories, but when I saw this I just got pissed! While I think the content is good, I have never known, nor have I ever told my clients to do any of this stuff or given any of these "pieces of advice" other than the cool down one. Yes, there are some extremely irrisponsible trainers our there so I think that trying to educate everyone about what makes a good vs bad trainer is a good idea, but the tone of this article makes it seem like ALL trainers say this stuff which is simply not true. If you can't find a scientific basis for anything you tell your clients or any thing you trainer tells you, then you probably shouldn't be doing or saying whatever it is.
And cool downs are imporstan for a flexability stand point if you're doing resistance training. Weight training without flexability training will increase the risk of limiting your range of motion. However, as with anything in fitness it must be done responcibly and not in excess.