It's an interesting question, and though anyone doing research should be careful not to jump to conclusions, there appears to be a growing body of evidence that the problem is the physical nature of the game itself. There was a big deal made about this a year ago when three professional hockey players died in one off-season.
I can only speak about hockey, because I don't follow the NFL very close, but the players that lost their lives recently (both by suicide and OD), were players that were considered "enforcers". These were the players that constantly had to fight and got punched in the head a lot.
You don't often hear about offensive players (that are typically not as involved in the physical aspect of the game) speaking of having the same issues that the defenders/enforcers do unless they have been on the receiving end of multiple concussions.
How is it in the NFL? Like I said, since I don't follow football, I'm not actually sure if there are positions where the players are more likely to be hit in the head. If there are "enforcers" that typically are the ones getting hit the most, and these are the same players speaking of depression, and killing themselves, then perhaps it's possible that the cause is in fact just due to years of trauma to the head.