No, it's Biden's prerogative to call for a vote to override the Parliamentarian. It still takes 60 votes (or, it could be 2/3rd - I can't remember which) in the Senate to overrule the Parliamentarian.
Hmmm. That’s interesting. I am not an expert in the rules...I had just read that. What I read was that Biden could do it unilaterally. The SHTF if the Dems pull that.
On the other hand, I can’t see the Parliamentarian ruling against the ruling class in the first place. But, could be a non-partisan office?