As an A330 captain/instructor/check airman and author of numerous training materials on the A330, here's my take on the Pop Mechanics article:

Overall a pretty good article, but there are a couple of technical errors in the article and comments.

One statement is certainly correct: "Bonin's behavior is difficult for professional aviators to understand."
If the two pilots had simply sat on their hands when this incident first occurred, it would have all come out OK. There have been a number of similar loss of airspeed incidents due to the particular model of pitot tube (all since replaced). The incidents last only a short while. In all the other cases, competent pilots continued to fly the airplane in a normal pitch and power combination with no ill effects.
This was not a sidestick issue. In my opinion, this was a pilot competence issue. This is not a Boeing/Airbus issue either; Boeings have also stalled at altitude and subsequently crashed. It is inexcusable for the stall warning to have been going off for so long without positive nose-down input from the pilots. There is no extra energy to make a level flight (or climbing) stall recovery at altitude. A nose-down recovery is the only thing that will allow the angle of attach to be sufficiently reduced for a return to normal flight. At 2:10:30 they were well on the way to a recovery, but apparently failed once again to understand basic aerodynamics.

Consider also that the stall angle of attack at high altitudes is greatly reduced from that at lower altitudes (due to several somewhat technical aerodynamic factors outside the scope of explaining here). Having flown (and taught) high altitude stalls in an A330 simulator, it is not difficult to recovery from a stall in this regime, but the pilot has to actually DO IT.

When referring to TOGA "I'm in TOGA, huh? " he is referring to the TOGA position of the thrust levers - which is the full forward position used primarily for full-thrust takeoffs and go-arounds (as well as emergency maneuvers). Note that the engines are hung below the center of gravity; this produces a nose-up pitch moment, which also can reduce nose-down elevator authority. Had they actually pushed the stick forward (which they didn't for very long) they may have also needed to reduce power to aid in a timely stall recovery. This is the standard stall recovery now being emphasized in airline training.

"Thanks to the effects of the anti-icing system, one of the pitot tubes begins to work again. " The pitot tubes are constantly heated. This model of pitot tube was replaced with another about the time of this accident (some airlines faster than others). The internal geometry of this pitot tube is primarily responsible for the clogging - not a heating issue. Pilot selected anti-ice refers to engine or wing anti-ice.

When in dual input mode lights in front of each pilot flash illuminate to show that both pilots are making sidestick inputs. An option exists for an automatic warning to say "Dual Input" when this occurs. I don't know if AF had that option. Each sidestick has a button that allows that sidestick to override the other (the last one pushed has control). The same button also disconnects the autopilot. The override button is intended to override faults, and allow a complete takeover, not solve a fight over who has control (not that there was one). Airline pilot discipline is to be very clear on who is flying the airplane - and as we see in the article, when a transfer of control takes place , e.g., the statement: "I have the controls."

In alternate law, the same pitch law applies as in Normal law.That is, g-load/pitch rate demand. When the sidestick is in neutral the airplane is essentially stable in pitch. The pilots would need to push the stick forward to reduce the angle of attack and recover from the stall. The airplane would not pitch over by itself Cessna 172 style. But these airplanes are designed to be flown by professional aviators with training in these factors and type ratings in this airplane. The transcript indicates that there was a lot they did not understand.

As mentioned in one comment the stabilizer trim was virtually full nose up. This is a result of the sidestick being held back for a long period of time - not some design flaw or data error. (the flight control system moves the elevator to meet pilot demand, then automatically trims the stabilizer for efficiency). The full nose-up trim reduces the nose-down elevator authority - as it would on any airplane. Again, this may not have actually been factor since they didn't command a nose down attitude for the recovery anyway..