-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.

Dropping stones in a bucket is "technology," effectively.

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.