I suspect that this might be more accurate, in that several times folks put things there and took them back. There are interesting questions about sand deposits and the history of the island, and of course if it was a "good spot" to bury treasure during a time of privateering then perhaps there are several interesting places. Some of the more elaborate underground construction though seems to be in support of prohibition[1] (well in support of smuggling in liquor during prohibition).
A couple of things are hard to dispute, square cut timbers don't just "appear" underground, so someone put them there. But it could be for much more mundane reasons (like gold mines in the Sierra Nevada Mountains)and it makes for a spicy tale to through in pirates.
You're assuming the original descriptions are trustworthy and not heavily biased. Yeah, maybe they were 'square-cut timbers'... or maybe it was driftwood and they were desperate to find something (see the 'treasure chests' in https://news.ycombinator.com/item?id=8149351 ), or maybe natural processes produce squarish timbers (are the Giant's Steps produced by giants?), or maybe the original reports of squarish timbers were made up (wouldn't be the first time, to say the least).
Everything you say is true, and it could all be one giant hoax by some land owner who said "I know, I bet if I make up a great story I can sell this worthless land for a few bucks!" What I did, and its useful for any story, is to make a "Charitable Assumption" which is to converse on the topic with the assumption that the other party is being as truthful and/or as accurate as they can. By doing so we can engage in conversation and perhaps learn new things. The trick is that one can make a charitable assumption and continue the conversation without believing that the assumption is "true" in the literal sense. It is sort of like a temporary stipulation for the purposes of discourse.
If we take the story at face value then the existence of non-natural artifacts, both timbers and other things, are considered "true" during our discussion. Then we can explore alternative reasoning (or even carry the existing reasoning further down the path) as to how or why that came about. What is important here is that there is no compulsion, either explicit or implied, in that sort of discourse that "forces you to believe" something which you don't.
You gotta decide which story to take at face value, though. In some versions it's only one layer of wood of unspecified shape and arrangement. In others it's layers of wood at regular intervals. In others it's specifically square-cut timber. Generally the more recent retellings of the tale have more of these juicy details than the older ones.
The thing about a good story is, it's hard to resist the urge to make it even better.
The choices aren't only "true" or "hoax." gwern pointed out that it could be due to wishful thinking, or lack of knowledge about certain natural events.
Those last two accept that people are "being as truthful and/or as accurate as they can", but also recognize that people are imperfect observers and imperfect interpreters. As your charitable assumption doesn't allow for something that we know happens frequently, I think it's fair to say it's a non-realistic assumption.
For example, astronomers from Schiaparelli to Lowell said there were canals on the surface of Mars. Some made quite detailed maps. There was no hoax, only a combination of wishful thinking and optical illusions.
At some point we have to stop being charitable in the way you mean. But we can still be charitable by saying that people are imperfect. This path, which gwern took, also leads to learning new things, though about human psychology and not putative pirate treasure.
A couple of things are hard to dispute, square cut timbers don't just "appear" underground, so someone put them there. But it could be for much more mundane reasons (like gold mines in the Sierra Nevada Mountains)and it makes for a spicy tale to through in pirates.
[1] https://www.google.com/search?q=prohibition+tunnels