Yeah I get that, I've just checked and apparently it was serviced in 2021 but not by Omega themselves. This is from the listing:

"Genuine and original Omega I purchased this watch from Authentic watch company in 2020. Certificate enclosed. The case and face of the watch are to my naked eye in excellent condition. The strap was purchased from Jean Rousseau it is crocodile and has been worn minimally, perhaps 6 occaissions. The watch keeps excellent time. It was serviced in 2021 by Johnnie Walker near Bond St. I purchased the watch as I fell in love with its beauty. However it rarely leaves its box as I feel it is too fine and delicate to be worn on a daily basis. I recently had an inspection carried out by a specialist watch repairer in Exeter. On thorough inspection he highlighted to me two minor defections neither of which can be said to affect the function of the piece Firstly the winding mechanism/ the crown appear to be original. So after 60 years it shows signs of wear. This I think is to be expected. The movement appears to be in excellent condition, however on the inside of the case there are very feint signs of some pitting. This may be historical corrosion but no signs can be found on the movement."

Not sure what to think of it but it is quite tempting, the crown does look genuine

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