Exactly. There is nothing binding about the Parliamentarian’s ruling.
The GOP fired the Senate parliamentarian over reconciliation in a 50-50 Senate in 2001. It was such a non-scandal that NYT's reporting on the GOP replacement was a 57-word stub on the bottom of A22.

Feb 27, 2021 · 3:40 AM UTC

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Replying to @marwilliamson
My feeling is this was an excuse to leave the minimum wage increase out as Manchin and Sinema would have had their feet put to the fire in states that really could have used the increase.
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Replying to @marwilliamson
Shhhhhh!!! Don't say that too loud! Americans might figure out that Biden/Democrats never really cared about passing the $15/hr minimum wage. It was just a good marketing tactic to reclaim the presidency.
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Replying to @marwilliamson
It’s just an excuse. They don’t want to do it, is the truth.
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Replying to @marwilliamson
The less Americans need to know about how the sausage is made, the better the government they will enjoy. Nobody is enjoying any of this, except for the people performing this second rate production. And they want a raise.
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Replying to @marwilliamson
Came at a cost though
Majority Leader Trent Lott fired his parliamentarian nytimes.com/2001/05/08/us/ru… (Then two weeks later Jim Jeffords fired Trent Lott from being Majority Leader latimes.com/archives/la-xpm-… )
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Replying to @marwilliamson
No but at least 2 democrats aren't on board, then we just screwed ourselves
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Replying to @marwilliamson
Sadly, it’s so much we told you so
Replying to @marwilliamson
Any blue excuse will do.~
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Replying to @marwilliamson
GOVERNING IS VERY DIFFICULT.