At the moment one hot name in jazz field is Cory Henry, playing both hammond organ and piano. His international breaktrough was his amazing synth solo in Snarky Puppys "Lingus" (see here: https://youtu.be/L_XJ_s5IsQc, solo stars at 4:20)
Here we can see a closeup video of his piano playing, which is interesting technically: https://youtu.be/gEEph4GBXF0
Obviously he is playing lot with straigt and even hyperextended fingers. I believe this comes at least partly from his hammond background. Interestingly enough you see this kind of technique more with afro american jazz pianists (bebop legend Thelonius Monk being an ultimate example). I believe it's perhaps because of lack of classical training. And I am not saying that this is wrong or bad, quite contrary. Obviously (just see Cory Henry's example) it works quite well. They may have started to play just naturally without mantras like "curve your fingers" which are common in classical field.
And finally, I believe that this kind of an ultimate talent comes forth no matter if she/he has proper education or teacher...
Agree! Whatever floats the boat. I like this style of playing, quite expressive. I am always thinking we should really spend more time feeling out the piano, before and while we play. It could be the sheer size of the instrument that inhibits us from feelin it out, say the way a violinist feels/handles the violin, chellist -> chello..