-That depends on how you use them; this is a people problem, not a tech problem, as you (IMHO) correctly observe.
If you use the voting machines to keep a running tally of votes cast so results are available immediately after polls close, you have already gotten a large benefit from them.
However, to ensure the (most warranted!) concern of the electorate that the votes are not being tampered with, the machine should also print a receipt to the voter after his/her vote is cast, in a human-readable format, which is then deposited in an urn much like today.
So - you get instant results, and if the result is challenged, you can audit the actual ballots rather than just doing a code audit and hoping the numbers haven't been tampered with in some undetectable way.
Paper slips signed by an independent observer and marked with indelible ink can be audited more easily by electoral participants than counting featureless stones in a bucket.
They have the added security feature of oily fingerprints containing unique DNA imprinted on them. It's customary in functioning democracies to not sequence fingerprints on a ballot paper, but theoretically it could be done.
If you use the voting machines to keep a running tally of votes cast so results are available immediately after polls close, you have already gotten a large benefit from them.
However, to ensure the (most warranted!) concern of the electorate that the votes are not being tampered with, the machine should also print a receipt to the voter after his/her vote is cast, in a human-readable format, which is then deposited in an urn much like today.
So - you get instant results, and if the result is challenged, you can audit the actual ballots rather than just doing a code audit and hoping the numbers haven't been tampered with in some undetectable way.