Birth date question

I have a 'wee mystery' concerning birth dates. I recently noted in the 1915 Scottish Valuation Rolls that James McIlhaggie's occupation was listed as Merchant Navy Seaman. My record of the family of William Carson McIlhagga and Rachel McLelland is that their fourth and fifth children were both called James and that their birth dates were 19 June 1881 and 19 August 1882. The most reasonable assumption is that the first James died before the second James was born. It was the second James who became the Merchant Seaman. However, in the records of Merchant Seamen on 'findmypast.co.uk' James McIlhaggie, born Greenock, has the birth date of 19 June 1881! So the second James appeared to claim the birth date of the first James!

Was he brought up to believe this was his birthday? Did he claim the earlier date (for which there would have been a birth certificate) in order to get in to the Navy a year earlier that he was permitted to with his real birth date? Or is there some other explanation? This 'wee mystery' deepens because his true birth date is recorded in the National Archives' Documents on line. I doubt whether there are any descendants who can throw any light on this. James and his wife Mary (Young) had two children. John Young McIlhagga/ie born 1909/10 married Margaret Smellie Allan in 1931 and they had one daughter, Margaret Allan McIlhagga who died as a young child. James and Mary's second child was Jane Young McIlhagga/ie who was born in 1911 and if she is still alive will be over 100 years old. I have no information that she ever married.