Fiber is biodegradable, so wherever you blow your backwash water, it will break down. DE is petrified microorganisms, and since it hasn't decayed in a million years it won;t now. It will just leave a white crust where it lands. That's why I use fiber in my DE filter. I can backwash onto the front lawn.
There are probably ordinances somewhere about discharging backwash with DE in it. You could probably argue the case since cellulose is just highly refined sawdust.