The ballot voting process is also misunderstood by regular citizens, even nerdy ones. From experience, even by voting officials.
Any citizen can go and check how votes are counted in their Geminde. Any citizen can check what is reported in the federal tally. I did several times. It's not rocket science.
Technically you don't even need that, you just need to be able to count, i.e. find the successor to a given number.