As others have said, Sony have far from a majority share - all the other members would vote to sell BD's to Nintendo
Regardless, assuming Sony owned it >50% - if Sony were to use their power in one market in order to gain an unfair advantage in a compeltely seperate market, that would come under anticompetitive behaviour, they would be sued for a LOT of money. Just as google can't tinker with it's google search algorithm to preference pro-Android websites. The alternative is they just license it out and make a tit ton of cash.
Regardless, it's ridiculous. Nintendo have developed a proprietry storage format for every single one of their handhelds and home consoles. They will not break this pattern.
Edit: Fixed Typo







