ADVICE, NOT A COMMAND

That apparently is all the Senate Parliamentarian can do.

NYT:

Technically, Mr. Frumin’s decisions are not binding. But Senate leaders almost never overrule the parliamentarian, so he will effectively have the final word.

LAT:

(It should be noted that the parliamentarian doesn't rule, he advises; and he can be ignored by the chair, though that rarely happens. This does not stop the aggrieved party from blaming the parliamentarian, however.)

Boston Globe:

The Senate has generally not overruled the parliamentarian’s decisions, but it is possible.