Just throwing out my opinion on this coin-toss thing, but the after taking a day to think about it I believe the Giants rightly should have opened the stadium, anyway.
Look at it this way. Not only have the Giants been around since 1925, giving them 35 years of football seniority over the Jets, but the very nature of their stadium partnership favors the Giants. Yes, the cost is split 50-50, but the idea for the stadium was put into motion well before the Jets ever took up the Giants' invitation to join them. And that happened only because the Jets' plans for the West Side stadium project in Manhattan blew up.
In other words, the Jets continue to ride behind the Giants. They may be equal partners as far as finances go, but the Giants were there first on all accounts. So, the right to open the new stadium's history should go to the Giants.
This whole coin-flip situation was unnecessary. If there even was a flip, that is. Still have no official word that it ever occurred.