Here is a link to the actual paper [1]. Their concluding statement was:
"Professional athletes are not immune from the growing obesity crisis and may not provide optimal role models of health. Concussions have drawn attention to overlooked long-term health consequences of sport participation. Increasing body mass in professional baseball players warrants similar attention for its potential impact on long-term morbidity and mortality because these players hold a special place as role models of health and human performance in our society."
Now, there are lots of big boys in the NFL that definitely have a couple extra pounds on them, which could also be skewing numbers.