Then you are just splitting hairs then. I don't remember what days the tweets were sent, but Trump was definitely asking Pence to count votes from an alternate set of electors than the ones who had already been legally chosen. But even with what you are saying, Pence did not have the constitutional authority to reject votes from those electors. Does it make sense that he would have the power to influence the outcome of his own election in such a way? Wouldn't that be a massive conflict of interest?
When it comes to settling disputes, this is how it works: if at least one senator and one representative object to the results from a given state (this happened on the 6th), both chambers vote to sustain or reject the complaint. Only if both chambers sustain the complaint are the results thrown out (that didn't happen). When it comes to counting the votes, the 12th Amendment says, "The President of the Senate shall, in the presence of the Senate and House of Representatives, open all the certificates and the votes shall be counted." The Constitution gives the Vice President only one role in this process, which is to open envelopes for those votes to be counted. There is no assigned role for the Vice President other than that.