Elledan, the Dutch news site is wrong. To be sure of climbing over an ITCZ "lightning storm," the AF flight crew would have to have assumed they might well have to climb as high as 55,000 feet or so, and to do that, they'd have needed the Space Shuttle, not an Airbus. Their sudden climb to 380 had nothing to do with any attempt to top a thunderstorm.
Yeah, that's what I figured. Pilots can fly around a storm, but they can't fly
over one. No idea why this news site (usually very reputable) made such a big blunder. Their claim struck me as odd as it was never coined as a possibility elsewhere, especially not on this site
The current conclusion seems to draw towards pilot error with equipment failures and gaps in training as likely contributions. The nose-up inputs especially seem beyond merely curious. I really wonder whether there might be anything about that on the CVR.