Voter ID only takes care of controlling the input to the voting system.
It does not control the means of COUNTING the votes.
Votes can to e deducted from one candidate and added to the other.
t oe = be
You are absolutely correct. Counting votes is another issue altogether. But counting, even if 100% honest, won’t help when fraudulent ballots (votes) are already present.
However with paper ballots, it is possible to hold the counting process reasonably honest by posting good observers.