As those who have taken one of my Handguns 101 classes or Shooting Skills Tuneups may recall, I try to get students to know how to use BOTH methods - or in some cases, the "overhand" method (a variation of the slingshot method). One of the reasons for my emphasis on primarily using the slingshot (or overhand) method to chamber the first round is that it helps ingrain a skill set that is very important when the time comes for rapidly dealing (slap, rack, ready) with the most common stoppages.
Much of what is stated in the article (and here) is rather "generic". No one know more about the guns than the folks that made them, so their instruction manual should super-cede. Kahr Arms, for example, often says NOT to use any method except the slide release to chamber the first round. And for good reason. For some people, anything else can cause the slide to fail to go into battery (close all the way). However, for many shooters with some common Beretta semi-automatics, the thumb safeties mounted on the back of the slide can make the sling shot method quite painful on their thumb and/or index finger - and therefore impractical.
A good friend and I did a little more "break in" shooting tonight with a semi-new Ruger LC9-S. The slide lock/release on it is still so tight that the only way either of us could drop the slide was via the slingshot or overhand method. Making the point, once again, that the only way to really know how to "run the gun" under even a little stress is to DO IT. Preferably fast and frequently.
Feel free to chime in here on what works best for you.