I look at it the "potential fallout" issue this way, which seems to be the same general way that Josh outlined it in his public statment.
If you have good reason to believe a player did something wrong, then you don't play him.
When a player has been arrested, you need to presume (but not conclude) that he (or she) did something wrong. Suspend. Then investigate. If investigation leads you to conclude (with for example, 75% certainty) that the player actually did NOT do anything wrong, then lift the suspension. BECAUSE YOU DIDN'T SUSPEND THEM FOR BEING ARRESTED, YOU SUSPENDED THEM BECAUSE THE ARREST SUGGESTED THAT THEY DID SOMETHIING WRONG.
What about the fallout if the person is later convicted? If you acted in good faith (as evidenced, for example, by the decisons being made independently, not by the athletic department), then conviction is unlikely: if the totality of the evidence suggests that the player did not do anything wrong, then it's unllikely that a jury will find, beyond a reasonable doubt, that they did. Sure, a conviction might happen anyway. But if you honestly believed that the player did nothing wrong, you shouldn't be ashamed of having allowed them to play (and, could, instead, be proud of having respected the presumption of innocence).
So yeh. If an independent assessment of the evidence indicates a fair degree of certainty that he did nothing wrong, then let the world know that, and let him play. Regardless of the status in the criminal system.
If the conclusion is that he likely did do something wrong--whether as charged or not--then punish him for that accordingly. (Personally, I don't see a need to wait for the legal system.)
The public statement should, of course, NOT disparage the complaining person, the police, or anyone else. "The charges were indepently investigated, and we are confident that that the player did nothing wrong", not "The charges are BS."