I've been contacted by the owner of the watch who has provided clarification as to the ref numbers. The watch has been in his family since new and has been regularly serviced by RSC. The ref between the lugs is 1802 and interestingly enough the ref on the case back is the equally rare 1804 rather than the more common 1803. Rolex propensity for mismatched case refs and casebacks refs is well known.
So please rest assured this is an honest watch and bid accordingly.
Here's a recent RSC card...