I've had a nylon anchor rode catch my keel in light wind & current driven situations. A small kellet will keep the unloaded rode straight down - if the boat does do a pirouette, the rode just passes under the keel and rudder.
With a chain mooring, the chain will hang straight down until you put a load on it. I can't imagine a scenario where it would foul the keel. An examination of the keel should tell the story. Either it has chain marks or it doesn't.
More likely is that the boat sailed around the mooring all season and tied the chain into a Gordian knot around the anchor shank. This effectively reduced the scope and allowed the wind and tide to drag the mooring. Examination of the mooring should tell the tale. Might be worthwhile to have a diver look at things - would be nice to know what happened.
Years ago a friend on a nearby mooring used an unusual system - 3 Danforths set in a star pattern connected by chain. Seemed like a lot of trouble to set, but no problem with things getting tied up in a knot.