Although both hemp/linen and wood contain cellulose, they are structurally very different. In wood the cellulose fibres are bound together with a variety of lignins which resist the rot induced by micro organisms. Yew is particularly resistant to rot, but any wood buried under anaerobic conditions will in any case be protected. If strings were in the mud you'd think they would also be protected so it's possible that the archers were carrying all the strings with them when the ship went down and these were exposed to the water, as would have been any strings on bows in use at the time.
Cheers, Dave