Exactly! The machines that count the paper votes are extremely open to hacking. There is a vid on line. Totally observed by voting officials. 8 people vote yes and 2 vote no. The paper ballots are fed into the tallying machine and presto! The total count was 8 no votes and two yes votes... Totally undetectable!
I think this is the video you mentioned. If not, it still shows exactly why these computerized tabulators cannot be trusted.
http://dennismichaellynch.com/really-happening-votes/
I worked as an election judge for a number of years, but resigned last year, due to the hassles.
Anyway, if voters think that their paper ballot is safer than the touch screen, they are sadly mistaken.
Paper ballots are inserted into a scanner and the paper drops into a cabinet below the optical scanner. The cabinet is opened to hand count the paper ballots.
I don't personally don't know of any old style paper-ballots that are hand counted only and not scanned first. 
It is up to the parties to insist on canvassing the results to look for errors.