That link goes on to explain the actual perception people have and admits that it's likely valid (not that your average NFL player is more likely to commit a crime, but rather that they are way more likely to get off scott free for it). That the sport has earned a reputation for outright suppressing crime's committed by it's players is also pretty damning.
And as mentioned in the comments, neither of these are actually controlled for the various factors that people consciously and subconsciously find important. Like the fact that these people, by virtue of being quite wealthy if nothing else, are not the sort that are going to be targeted regularly by police the way the poor are.
For who they are, with all those factors being considered, and the rarity with which arrest leads to conviction, the fact that they are arrested at the rate they are is mostly definitely indicative of a crime problem.