Dan Worrall is well-known in concertina circles and has written a number of books and articles, all very thoroughly researched. On the other hand, the "professional pirate" linked to previously is clearly talking nonsense. The 'golden age of piracy' was roughly from the mid-17th to mid-18th centuries, a good 100 years before the concertina was invented (and for that matter, before the golden age of shantying). The association of the concertina with pirates is entirely a Hollywood invention.

Concertinas were pretty ubiquitous in the 19th century. The ones the sailors (and other members of the lower classes) played were usually not the expensive fancy instruments you see played today, but cheap German-made ones which were more or less disposable. However the were small, light and fairly robust which made them ideal for taking on board ship (although the fiddle was far more common). They probably had brass reeds rather than steel, which would avoid the issue of rust.

Given that concertinas were found everywhere, it is nevertheless interesting why they are particularly associated with sailors. I wonder whether it is because sailors are seen as distinctive and romantic, and captured the imagination in the way that the 'Arries and 'Arriets playing concertina on charabanc trips to Southend or Blackpool did not.