Not quite: not all 1.0 players got the 'Legacy' opening and varied storyline in ARR, only those who passed a certain boss battle in 1.0's '7th Umbral Era' storyline. If you didn't pass that point, you started ARR like a new player (with the standard ARR opening on the ferry/chocobo carriage), only with the Legacy tattoo and all that old gear and levels/exp intact from 1.0 never explained where it came from.
But you are correct that eventually it doesn't matter anyway as by the end of ARR all adventurers, regardless whether they were one of the 'original' Warriors of Light from the Calamity that Louisoix teleported five years into the future, a pre Calamity adventurer who is not an original Warrior of Light, or a new adventurer recently arrived in Eorzea after the Calamity, all are anointed by Hydaelyn as a Warrior of Light, and that is what is ultimately important. Not what you may have or may have not done in the past, but what you have done now.
