....for whatever reason the crew elected to transit at 200' probably on the presumption that the lighthouse was at 47' - crucial in their decision making / risk assessment as no-one challenged it.
Even if the Lighthouse had been at 47 Feet AGL....a night transit over water in bad vis....using 153 feet (plus or minus Altimeter error, Radalt instrument error, Auto Pilot/Pilot height holding error) seems a bit bold.