To remove any ambiguity. The Electoral Count Act uses legally imprecise language by our modern standards. The applicable rules for Electoral counting are in one 275 word sentence for crying out loud. Here it is:
“If more than one return or paper purporting to be a return from a State shall have been received by the President of the Senate, those votes, and those only, shall be counted which shall have been regularly given by the electors who are shown by the determination mentioned in section 5 of this title to have been appointed, if the determination in said section provided for shall have been made, or by such successors or substitutes, in case of a vacancy in the board of electors so ascertained, as have been appointed to fill such vacancy in the mode provided by the laws of the State; but in case there shall arise the question which of two or more of such State authorities determining what electors have been appointed, as mentioned in section 5 of this title, is the lawful tribunal of such State, the votes regularly given of those electors, and those only, of such State shall be counted whose title as electors the two Houses, acting separately, shall concurrently decide is supported by the decision of such State so authorized by its law; and in such case of more than one return or paper purporting to be a return from a State, if there shall have been no such determination of the question in the State aforesaid, then those votes, and those only, shall be counted which the two Houses shall concurrently decide were cast by lawful electors appointed in accordance with the laws of the State, unless the two Houses, acting separately, shall concurrently decide such votes not to be the lawful votes of the legally appointed electors of such State.”
Nowhere in that does it give the VP power to act unilaterally.
Here’s the text of the entire thing if you want to read it for yourself.