It's not the senate generally that is taking the parlimentarian's advice in this case, but the presiding officer, who does get to unilaterally decide (although the have some options).
See 2 USC 641(d) for it being out of order and Senate rule XX for how those are decided (which is surprisingly flexible, as you hit). Or for a more readable source: https://www.cbpp.org/research/federal-budget/introduction-to...
But the fact that we're even discussing this shows that the article is pretty reasonable in calling this arcane.
