OK.. is it possible for the discharge hose to pop out on its own? It was pushed in quite far and has a "kink" at the end of the hose to make me believe it even went down far enough to bend around a corner... I ask only because it was completely out and no one says they pulled it out.

"...to bend around a corner". You probably constricted the outlet, pump came on, formed a jet and Newtons 3rd law came into effect. Shorten the hose and use a connector to keep it in place. There is a lot of force from a washing machine pump and what you describe is not uncommon.

Yes its possible mine does all the time and ive tried pushing it in as far as i could then a few washes later its out again