The requirement is not "accurately count the votes". It is: "Allow people to vote, and have their votes counted, in a demonstrably fair way, so that an average person can have high confidence the outcome is fair, given the adversarial nature of the system and varying levels of education / honesty among all present".
A election only means something because of the consent of a large number of average people to abdicate their freedom to someone else based on what they feel was a fair process.
In Ireland, observers from multiple parties observe the votes as they are counted and publish their own numbers realtime (see tallymen).
In this context it's very hard to argue the vote was rigged...