The key point is SUPERVISION. Yes, the voting station staff might be corrupt, but if you have representatives from each of the parties with a stake in the election present during the entire voting and counting process, then sleight-of-hand becomes is much trickier.
With a pencil-and-paper-based system, you need to distract a great number of people *on election day* (assuming the votes are counted immediately after polls close, as in the UK) in order to 'interfere' with the vote.
With the electronic system, all you need is a moment alone with the machine, at basically any point after its manufacture, to make your modifications (whatever they may be - software/hardware - just preferably hard to trace) - and it suddenly doesn't matter how rigorous the supervision is, come election day. Human beings can't supervise at the electron level.