Having a 1.0 character with a legacy tattoo isn't the same as having a legacy account (confusing I know...)

There also wasn't a quest to get the legacy chocobo. To get a legacy account (and in turn the legacy chocobo), you had to subscribe for at least 90 days between 6th January 2012 and 29th September 2012.

It sounds like you simply didn't subscribe for long enough during the qualifying period so your character has the tattoo from being from 1.0 (any 1.0 character gets the tattoo), but your account isn't marked as legacy so no legacy chocobo. If it was you'd see a special symbol on the character selection screen as well as you received a reduced subscription fee as well.