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That's dumb. You can eat wild meat and take precautions to avoid getting rabies at the same time. You get in your car, but you look where you're going and try to drive safely, you don't drive with a blindfold on.
Sounds like a rubbish claim since rabies is routinely said to only occur if an animal bites you.
I am always wary of bogus claims that wild animals are infested with dangerous diseases. These are always hysteria-driven PR-inspired articles originating from the farming industry who basically want as many wild animals removed/killed in the countryside, solely because they paranoidly believe that wild animals are pests which are a threat to crops and domesticated animals. A classic example of this was the extreme hysteria about the mythical threat of TB to cattle from wild badgers in the UK, a while back.
Rabies is most concentrated in the brain and the salivary glands of a symptomatic animal, but it spreads to all the organs of infected animals.
One point on the roadkill thing though: Rabid animals have less self-control, so they could be more likely to end up as road-kill.
Also: There's no reported resevoir of land-rabies in the UK or Australia, only in bats, and the occasional times an animal gets infected by a bat. Everywhere else there's resevoirs of rabies in land animals.
Of course wild animals become infested with dangerous diseases. Not the healthy ones. Lots of wild animals get these diseases, but they die from them.