The rules are if the count is close then there is a re count. When you RE due something that means that you are repeating that same process.
The second time they counted they added in more ballots, thus making it a new count. That new count was a closer margin than the first time they did it. By those same rules this NEW count with NEW ballots should have had a re count to make sure.
In Washington they did 3 counts. The first two counts the democrat did not win, by the third count they found ballots in some basement, added them and bingo the dem won and they stopped counting. Strange part is that more people voted in King County, Washington than actually live in the county but what the heck... The dem won one out of three counts so she got the job.