I'm perfectly happy with Rafe's answer. It's not that the Dragon can be someone other than Rand. It's that it's an old Prophecy, as others already said.
People argue over every single line of text in the Prophecies of the Dragon, except that specific one? We argue what slaying people with a leaf means, we argue over what "Breaking the world again" means. But not one person ever goes "What if it's not an obvious man reborn?" Specially combined with a world that is largely female dominated due to only women having magic and influencing things....
I never took it as "OOh, maybe it's not Rand." I took it as people are dumb and history gets foggy and that leads to mistakes.
Spoiler
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Alanna and her Warders
in Wheel of Time TV Show
Posted · Edited by AyutaYamane
Yeah, I agreed with you.