The Chain are sailing in what they *thought* was Legend's Hyrule- on their way to Hyrule's shores, when a sailor shouts "MAN OVERBOARD!"
The Links on deck immediately race over to see a teenager dressed in green unconscious and draped over a large plank of driftwood. They pull him up, and brush the wet hair out of the boy's face to see... Legend.
Well, the Legend of the Hyrule they are currently in. Because it is Legend's Hyrule. Just not yet.
The next week or so is spent with Legend staying as far away from his past self as possible, while the other Links take turns tending to their friend's seasick, dehydrated, and delirious past self.
Legend has no memory of this happening in his own past save for perhaps a few blurred memories that could have passed for fever dreams, or the sailors of the ship they were on.
The Chain are the ones to deliver Past Legend to Fable safely. Mayhaps Fable remembers this, and trusted the Chain when they first showed up to pick up Now Legend at the beginning of their Quest? Perhaps that is one of the reasons why Legend joined them... his princess trusted these strangers, knew who they were, and was confident that they were a safe group. Maybe she is the only Zelda to recognize the Chain as Heroes of the Past and Future? Because they explained who they were when they brought her Hero back from his disastrous voyage at sea...