that's certainly not true as a blanket statement. I was on a flight from SFO-ATL, with a final destination of MEM. We had a medical diversion to MEM so I disembarked after they offloaded the patient. I had given my sport coat to the FA and she had it in the closet.
Now, I forgot to pick it up on the way out, but are you suggesting Delta had no responsibility for this item? They had possession of it, they knew EXACTLY who it belonged to, since the FA knew which seat I was in. I filed a lost item report as soon as I got home, before the plane even made it to ATL. Never got the jacket back, of course.
Just because FA helped by putting it in the closet doesn't mean they had possession of it. If the FA helps you put your luggage in the overhead, do they have possession of it?
BTW I agree DL lost item handling sucks. Ever since they contracted out it seems no one at DL cares about getting lost items back to owners.