I don't know the full facts yet as I have only just started researching the subject for part of my dissertation next year.
I don't know how hospitals work in America but in England we have the Freedom of Information act, where you can ask for details on most things and providing the information is there they have to supply it. Anyway, with a years worth of data 64% of A&E admitance (British version of ER) was through binge drinking - mostly where people have drank too much or got into fights. 6% was due to football (soccer) injuries, 3.5% was due to other sporting injuries, and less than 1% was due to mma related injuries.
Obviously some things to consider here are:
1. These are statistics relating just to the hosptial from my area.
2. It doesn't explain why - but one reason could be the popularity of the sport compared to others.
But at least these help to support your statistics