Well...except that by all accounts it probably isn't true...Hillary wore a Smith's on his wrist and may have carried a Rolex in his pocket. Tenzing Norgay was supposed to have worn his personal Rolex, a gold datejust - not an Explorer prototype. Hunt didn't summit and it's unknown what watch he actually wore. Rolex supposedly lent watches for testing for the expedition, but only Norgay's personal Rolex is the only one known to have been worn during the '53 Expedition.
So...if you want a true explorer's wrist watch, worn on a wrist, you want a Smith's Everest PRS-25...or I guess a Rolex Datejust circa 1952.