I don't know if your argument would hold up. Although yes you can legally hunt game with a dog its not defined that off leash is mandated. I'd have to double check but aren't blood tracking dogs for deer to be leashed? There are some care and control regulations that might also pertain.
I can understand the need to demonstrate care and control of your dog in a multiuse area I'd be happy if the guide line was amended to read leash or e-collar.