You must be confusing levers with scanners there Brooklynite.
Unlike levers, scanners can generate phantom votes all by themselves. See:
http://www.nydailynews.com/opinion/voters-damned-article-1.1028275
And see Harri Hursti's scanner hack from years ago, which should be common knowledge by now:
http://www.votetrustusa.org/index.php?option=com_content&task=view&id=798&Itemid=51
Doesn't matter what the zero tape says! The scanner can have votes in the machine without anyone knowing.
As far as your lever counter experience, we have election laws that say how to run lever elections in NY, or at least we used to. And they state exactly how and when to check those counters, which CANNOT increment by themselves the way scanner counters can.
But I agree this latest move to levers is not necessarily about election integrity. It's about avoiding the possibility of a HAND COUNT of paper ballots in the event of a close City-wide election. The rest of the state gets to avoid hand counts, so why should the City be the only jurisdiction to have to find out who won their close elections? Answer: because the City Board of Elections wrote regulations to do so. But this time, they don't think they can enforce their own rules because there are so many paper ballots and so little time. (Note: Columbia County counts ALL votes by hand, no matter how close their elections appear to be.)
If you want to use paper ballots, you have to be prepared to count them by hand, and to find a way to know when this is necessary if you do the first count on scanners. We don't have any of that in NY, or any other state that I know of except for some elections in New Mexico, and it's possible we never will. In that case, lever machines are far more reliable vote counting devices than ballot scanners.