Indeed, and the math is the same. If out of 3 million voters, just 1000 double-check the printout, they will detect a 1/100 flip with probability 99.996%.
My preferred machine would be one that did not use integrated circuits, but was simple enough that the entire board and circuit was visible - with no software beyond the circuitry at all. You just need a very simple sensor and tally wheels that mechanically advance, like those used for measuring wheels etc. No need for memory. Keep automation to the absolute bare minimum.