Like Dan, I have dozens and dozens of snapping turtles in my 6-ish acre pond, and also like Dan, most won't fit in a 5-gallon bucket.
They don't bother me at all, and I don't think they do any damage to the "healthy" fish population.
Excerpt from Robert Crais' "The Monkey's Raincoat:" "She took another microscopic bite of her sandwich, then pushed it away. Maybe she absorbed nutrients from her surroundings."