If Michael Vick can own a dog again, a non-violent felon should be able to bowhunt. & +1 on all the hypothetical and real life examples shared above.
What about that guy in NJ, Armando Pioppi Jr., btw, who was falsely accused and convicted with poaching the giant buck he legally shot. There was a story in D&DH on it this month. He had a dozen or so friends and neighbors he called the evening he shot it and served as witnesses and defense. All the evidence points to his innocence and despite that, the COs, so-called forensic experts, and his own lawyer basically screwed it all up. I encourage you to read that story if you can. It really shows how someone who is innocent can have the system fail them based on an "anonymous tip." It also shows you what to do immediately if you ever shoot a record book animal and how to defend yourself from personal and legal attacks.
That's getting a bit off subject, but it does go back to the point that you can's just say "he's a criminal," no bow or hunting privledges. It's simply ridiculous.
Along these lines, Minnesota has a law where the COs can confiscate your hunting equipment, vehicle and/or boat upon charging you with a hunting or fishing violation. They just take it, regardless of whether you've had a chance to prove your innocence. Your bow gone, taken away for the remainder of hunting season based on an alleged violation, which is often found to be baseless. Ridiculous.