[IshKebab]

No, you could do it in a way where the voter can verify their vote was recorded correctly but can't prove it to anyone else. Trivial method: require the voter to assign random numbers to each candidate. They remember the number of the candidate they chose. The voting system later says "you voted for 6".

[arlort]

And how do you avoid a scenario in which you assign 6 to candidate X but the machine secretly assigns 6 to candidate Y?

[IshKebab]

You have all of the recording done to a paper tape that the user can inspect as their vote is made. That paper tape is read by machine later. That means you only need to trust the counting machine, which is pretty easy because you can easily do random samples to check it is working, or have both parties count or whatever.

You can't eliminate the possibility that your paper vote is completely discarded and replaced by fake ones. But that's not really any different to existing non-electronic voting.