I've ate a few snapping turtles, along with hundreds of catfish, and this idea that both species need to be kept in clean water for a week to "flush the swampy mud taste" is hilarious. As with most other critters, a quick kill followed by removing the blood and guts and cooling the animal as quickly as possible are key to quality table fare. They're not some crazy beastly animal like some will have you believe and you can casually walk up to them and grab them by the shell with minimal risk.
It doesn't effect me that the harvest was banned, but I do wonder if this is was science or emotion based.