Link didn't believe a word that Lucia said.
Something about Zoran Lucia had exiled himself;
Something about there being no Lucia's family anymore, only the Archie family;
Something about the Mixed Corps being completely under the control of Sage Cody.
As long as the Lucia's family hasn't been wiped out, it's all bullshit!
The Lucia's family is used to saying one thing in public and doing another in secret.
Link only believed in his own convictions and his determination to kill Zoran Lucia.
Did they really think Link had forgotten about the ordeal he went through when he was hit by three Star-annihilating Cannons?
If it wasn't for the need to further his studies at the Academy Headquarters, and if Dean Frist hadn't refused, Link wouldn't have cared where Zoran "hid". He would have sought him out and killed him before he was promoted to Sage!
He would definitely not have allowed it to end like it just did, with only a war of words.