Welcome to the forum. Sorry that happened to your SIL. Have you checked the GFCI receptacle in question to see if its trip and reset are working? Older GFCI can fail numerous ways, including indicating tripped and still providing power to the receptacle and anything load side, and perhaps fail to trip if line/load are reversed. Was the Cuisinart plugged into the 20A GFCI receptacle visible in pic #1?
As of 2015, GFCI are required to self-test and lock-out on wiring errors or self-test failure. Your understanding of how GFCI is supposed to work is sound; the first thing I'd do is replace the receptacle with a newer (2015- on) style.
On an aside, I've never seen a heating element warp like that.
As mentioned above, there is the chance she didnt see 6ma current. and if she had one hand on the Cuisinart and the other on the stove, that's a hand-to-hand hit and extremely unsettling to downright painful. Still, my first course of action is change the receptacle, then call Cuisinart for any warranty you may have. Even if the unit has run past its warranty, they may want to see the picture of the warped element and reimburse you.
Electricians do it until it Hertz!