Even for the paper side. Most paper ballets are counted by machine so they could easily be tampered with at the count or when they're printed having a similar scale.
And recount-able by hand in case there is doubt.
Do you have a source for that statement? In Germany, ballots are counted by people making tally marks on paper.
Edit: Here you go. I couldn't find research or a study regarding it but this is probably good enough and was always my experience when I voted by paper: https://www.wired.com/2016/11/vote-counts-ballot-get-counted...
One reason is that Americans vote a lot more than Swedes. Here in California I have probably ~100 elections to vote in for each I had in Sweden.
It's quite common to drop handfuls of paper. And really, the grouping comes down to transportation issues as well; when you move ballots in boxes and trucks, 0(n) becomes less accurate.
There were numerous issues with the security, packing, and handfuls of paper in 2000.
http://www.dailymail.co.uk/news/article-3796116/Putin-s-part...
If you hack election software, you can change thousands or millions of votes as easily as one. The physical nature of paper means you have to work for each ballot.