Which is better for the individual people who might (and I stress "might," since the hospital denies it) have to wait slightly longer on a day he needs care? To wait slightly longer there, or to wait slightly longer because they had to route to a different hospital that's struggling to deal with the demand?
If you remove Langone from the situation, you're not simply left with "everybody gets seen one person sooner." That's a small-picture view. You're left with "many of these people just can't be seen here at all."
I'm not saying people have to like the rich. I'm just saying if I'm next in line after him at NYU Langone hospital, I'm glad I have that hospital to go to, even if that bumps me to 2nd priority in the room.