I find the dating of the fibre tricky, and it was no doubt used as packing for a long time. I'm also concerned about dates going back before 1500. However, it's claims about the trees that most concern me.
Assume that, in 1740, a 200-year-old oak tree is cut down. It follows that there are parts of this tree dating to 1540. The wood is seasoned for 20 years, and then used in 1762. A sample is taken and found to date to 1585. This is not the year the wood was used: it does not reflect the date of the operation.
A tree is cut down in 1700, so parts will date to 1500. The wood is seasoned for 20 years and used in the construction of a ship. This is broken up 50 years later and used in an operation in 1770. A sample taken dates to 1585. This is not the year of the operation.
A similar argument may apply to the fibre. Coconut fibre from coconuts of all ages is collected and stored for a considerable time, and then used. So, the date of any sample will not be representative of the whole, and will certainly not reflect the year of use. Unfortunately, I don't know how long fibre might reasonably be kept in storage, or how much it might degrade in sea water.
If the samples have degraded then the dates could be way off. It’s simply that I’m neither confident about the dates nor the assumptions being made about the use of the samples. We don’t know enough about them.
I'm not pushing for any particular century, simply because of these questions. So, I'm not prepared to rule out 1762, though I'm not very happy with 1585. However, if people here wish to make claims based on the stated results of carbon dating, I really am quite happy to keep my thoughts to myself.