No, I think it takes 60 votes to overrule the parliamentarian.
The Chair (presumably Joe Biden on this occasion) issues his ruling, which can reject or accept the opinion of the Parliamentarian. Assume that Biden is in the tank for Obama, so he rules falsely that all this extraneous stuff belongs in the reconciliation process.
If anyone objects, the whole Senate then votes to uphold or reverse the Chair by a majority, only. And if there is a tie, Biden can vote to break the tie.
The point of the Byrd Rule is to prevent extraneous matters in budgetary process. But if the people in charge are willing to lie about it, the protection disappears.
John / Billybob