Note that this study uses a very small sample size, i.e. one college for four years, which is certainly statistically insignificant. And othere studies don't agree with that author. For example, the article mentions the study from Pediatrics magazine that says "'concussion rates were significantly lower in cheerleading than all other sports combined." There have been others.
Another big issue, as mentioned by UcMiami is that concussions among athletes often are not reported. For example, when Army, Navy, and Air Force put in new guidelines on concussions, the number of them doubled the next season - solely due to the guidelines. In football, where there are 22 players on the field in situations where many theoretically could suffer a concussion on any given play, it is very hard to notice potential concussions if the players do not cooperate. And in football, players traditionally have tried to cover them up in every way possible. I know high school football players who suffered five or more concussions without any coach or trainer ever knowing. My daughter suffered one in basketball and finished the game. Cheerleading concussions in many cases may be more obvious.
Because the data on college concussions is woefully lacking, about 30 colleges are involved in the midst of a major study on the subject, i.e. CARE:
NCAA, DoD launch concussion study