I've seen it mentioned most often regarding consuming crayfish. They carry a bacterium called
beneckea chitinovora, which is a common infectious agent. The majority of discussions I've seen on the subject seem to end with the recommendation that the practice of feeding crayfish should not be encouraged. One turtlekeeper (who I think is really knowledgable) suggests that the crayfish be cooked before feeding.

Crayfish are consumed readily in the wild by species such as snappers, maps and DBTs, though. And, in another forum, a member mentioned that this friends turtle got impacted from eating the shell of a crayfish and almost died.
This is just me, but even if they were only cohabitating with turtles, the fact that they can carry an infectious bacteria and eliminate waste in the same water turtles drink, wouldn't exactly make me want crayfish to be living with them. (And it would seem they're going to be ultimately eaten at some point, anyway.)
"You become responsible, forever, for what you have tamed." -Antoine de Saint Exupery-