Yes this is true. They're specifically expecting the same Hero of Time, and WW-Link is also specifically rejected as being the Hero of Time. I don't know if they expected him to travel through time or if they were referring to the spirit of the hero as Demise and Zelda do.
-Zelda, BotW (translation source: myself with help from a few others)
With this bond between the hero and the sword in mind, let's re-examine a few quotes from WW:
-Laruto, WW (translation source)
-WW intro (translation source)
I believe we finally have a definitive reason why the hero never...