This isn’t an interpretation, it’s taken directly from the Senate website:
As a staff official, neither parliamentarian is empowered to make decisions that are binding on the House or Senate. The parliamentarians and their deputies/assistants only offer advice that the presiding Representative or Senator may accept or reject;
https://crsreports.congress.gov/product/pdf/RS/RS20544
This article spells out exactly what these grifting cowards are doing:
Many leftists suspect that what the Democratic leadership is doing right now is similar — playing a “rotating villain game” where they let various figures take the blame for not passing important reforms. Sometimes it’s Joe Manchin and Kyrsten Sinema. Sometimes it’s the parliamentarian. But these obstacles aren’t really why the Democratic leadership isn’t passing these reforms. They just don’t want to — or at least they don’t want it enough.
That sounds cynical, but in this case, the truth is even worse. It’s not that Democrats are using the fact that they can’t do something they don’t want to do as an excuse. The more we look at the actual legal status and powers of the Senate parliamentarian, the more the real situation starts to look like this:
Black points his finger at Jones and says, “This is a gun. If you don’t do what I say, I’ll shoot you!” Jones grins from ear to ear and says, “In that case, I better do what you say!”