"So the age old question asking if a 2wd dually can get stuck in the yard on wet grass is.... Yes it can..."
Sorry, based on your description, I don't see it...
"put the truck in drive and proceeded to sink in mud up to the rim :/."
Seems to me, the wet grass didn't get you stuck, the rim-deep mud under the wet grass was the culprit!
I had my old 1994 Dodge CTD 3500 dually 4X2 on wet grass, in and out of pastures and hay fields (loaded and empty), on loose gravel, on wet forest skid trails, etc., and never got stuck.
Just lucky I guess.