Because the paper ballot system is audited live by all participating entities. The box that you put your ballot into is watched continuously by a member of your political party, by one state official and by a member of the at least one opposing party. Once the votes are in, then the two party people watch while the state official's team counts all votes and writes down the total. At this point they can take a picture of the final tally and send to party membership.

To mess with the election, you have to turn all three persons mentioned above, who all have conflicting interests [1]. And then do this for a significant fraction of the voting centers in one constituency to change the overall result. It's almost impossible to do this to any appreciable degree.

What more, explaining the above to regular people is as easy as repeating the above paragraph to them. As long as people trust that their party member's are not double crossing them, they will trust the process.

[1] the person of the opposing party might have ethics, so it's not given that they will just agree to blatant vote manipulation.