Earlier quoted context omitted.
Reporting just the percentages makes sense. Reporting rounded versions of those percentages not only makes sense, but is the universal idiom for reporting percentages. But reporting synthesized vote counts from the percentages --- even from non-rounded percentages --- is not normal. People on this thread are hung up on the reported percentages, but those don't matter in this analysis at all. They're not the problem.…
Maybe I don't understand what you have identified as the problem. My understanding of the article is that the raw tallies should not correspond to "precise" rounded percentages. The article in an addendum points out one way that could legitimately occur (some underling has the totals and rounded percentages but needs the raw tallies and naively multiplies to get them).
Steps (4) and (5) don't have any valid explanation, and few (though maybe some) plausible human error explanations.
As long as we're on the same page that nobody ever had any business reporting the numbers in step (5) --- they're completely fictitious! --- I don't have much to argue about here. The politics aren't interesting to me.