I would be a kill-joy skeptic and say that the "credibility" that you speak about, is merely the remote possibility of the ability. Ie.: to weave enough "what if's", and speculate "possibilities" and then your brain psychologically bolsters them because, .... gee .... it's *possible*.... There's actually a lot of credibility to this old legend. ...
So for example, in this case, you string together various salacious "what if's"
1) you note that mariner logs often do not survive today, of ancient voyages. Ok, sure. Granted. BUT THIS CAN BE SAID OF ANYWHERE IN THE WORLD , of historic times. Yet as you know, does NOT necessarily bode "treasure".
2) "unpredictable tidal bores and storms". Ok, sure. BUT THIS CAN BE SAID OF ANY OCEAN and history of the world. Yet does not necessarily bolter any particular individual treasure legend .... *just* because "storms occur". See ?
3) Lost ships and failed exploration attempts. Ok, sure. But welcome to the history of the east and west coast during European contact periods of those eras.
Heck, when storms erode the beach where I'm at (Monterey Bay) it's not unusual to see old ship ribbing sticking up out of the sand. From past boats and ships that were driven ashore during storms. But they're just ho -hum trawlers, fishing vessels, pleasure boats, etc.... That are no more than late 1800s in age, and have nothing at all to do with wealth or treasure etc.......
4) Have you been out to the Salton sea area ? I've spent a lot of time out there. Re. : Any speculation of "this was once underwater in the 1500s. And even after we toss in a few high tides, and storm bores to bolster the assertion, Yet when you look around at even the lowest elevation spots, you can never in a million years envision any ability of a ship (full of pearls no less) to just "happen chance" be able to get that far inland. You would have to have a very wild imagination, when looking at the lay of the land (and topographic maps) today.
Thus very "far" from credible.
The psychology that drives us to call these things "credible", is the same allure that, for example, makes so many people wax romantic about Oak Island : The faithful just toss out amazing speculations of motives, and amazing technological feats of *could have happened * (if you brought 100 slaves with you to dig, blah blah blah). And then presto, as long as you can find some far-fetched way something *could* have happened, then we all put skeptical critical analysis aside.
And the reason we do this, is that the lure of treasure is so strong, that no one wants to be "left out". Thus we brush aside inconsistencies, and brush aside more-plausible explanations. So too is it with the Pearl ship. Once the campfire legend is born, it's impossible to put to rest. No matter HOW implausible the story is, someone else can come along and conjecture the "perfect storm" and "nefarious sinister motives", etc....