I've had the same thoughts as you ... but this reference would appear to refute that solution.

"In 2011, the Auckland University of Technology compared the number of catastrophic incidents (i.e., resulting in paralysis or death) in rugby with other sports between 1975 and 2005. It found that with the exception of England, rugby incidents worldwide showed 4.6 catastrophic injuries for every 100,000 players annually.

The same Auckland University of Technology report showed American football resulting in 1.0 catastrophic incidents per every 100,000 players between 1975 and 2005. That’s more than 75% fewer incidents than the index tallied in rugby."