I don't believe this is entirely correct. The Constitution calls for the President of the Senate to open the ballots, which are then counted, presumably by the entire Senate, not just by its President.
Do you know what the problem with Georgia's vote was? I've read quite a bit about this period and don't recall anything about this.
I would assume there would have been a huge outcry had the President of the Senate arbitrarily rejected the vote of a state because in his sole opinion it failed to meet the Constitution's requirements.
Interestingly, of the 16 states in the Union at the time, 11 chose their electors either partly or entirely by vote of the state legislature.
Here's the Wikipedia take. Ackerman appararently thinks Jefferson was a little more devious but I haven't read the book.
In any case, "corrupt" is probably the wrong word to describe the situation.