Earlier quoted context omitted.
It seems to me that the "Hollywood bravery" you nicely describe really is bravery - Oxford Dictionaries says the word comes from French braverie or Italian braveria (boldness), based on Latin barbarus (c.f. barbarous). Alternatively it may be from bravo (wild, savage). Courage on the other hand comes from Old French corage , from Latin cor (heart). I think based on this the divers are courageous, not brave.
It's true that the word comes from those roots, but the Oxford dictionary you cite says plainly that the definition of the word as it is used today is: > Courageous behaviour or character. https://en.oxforddictionaries.com/definition/bravery Just as long as we all agree that cave diving is not about being that ridiculous Hollywood stereotype dude who deliberately breaks all the rules for no damn reason and it works o…
For the record the full OED favours the latter root for bravery (bravo braido, brado (wild, savage)). Strange they don't say the same thing.