Absolutely disagree. The position of "President of the Senate" has discretion, or it would not have been identified as necessary for the process.
The rules for interpreting Constitutional law require that the clauses of the constitution cannot be interpreted as having no effect.
Saying the President of the Senate is a rubber stamp, renders that clause as having no effect.
The Constitution does indeed clearly define the role and powers and does not grant the Vice President any such authority.
He’s not rubber stamping anything. He’s reading the results into the record. Period.