In Iowa, they started collecting ballots in boxes... from 'people on the ground', this used to be done with a simple raise your hand count.
this opens up a number of ways to easily 'juke' the vote. For example, some people might surreptitiously add more than one ballot into the box. They need not be obvious about this; they could have been handed blank ballots before the event by a single nefarious insider. Second, unless the box is shown to be empty before you begin, you have no idea if it is. I am not saying these things happen, but I am saying they could happen.
if you want me to believe your vote total at the end of the night, then at the very least, do an official head count at the beginning, and ensure that the totals match up. Also, have each ballot numbered, and when the ballot is counted, read out the number so that people can see their vote is accounted for.
That's just two simple ideas off the top of my head; I'm sure with any level of real discussion we could sort something very streamlined out that allows for anonymous, secure voting. If the goal is for people to trust that no fraud is going on, it's worth the effort. If, instead, it's assumed anyone crying vote fraud will be called a paranoid conspiracy theorist, then, well, you could probably even convince people to vote on a black box machine with no paper trail...