I am just theorizing here: Someone now takes the box of paper votes and runs it through the scanner machine. And passes this number along to someone. What is stopping them from tampering at this step? I think this is precisely what my co-worker was describing. There is an inherent trust that your paper ballot is scanned and recorded in a fashion that matches your vote.
An electronic voting machine could potentially communicate votes in real time over a secure connection. Or in the case of Brazil's machines, I believe stores it locally, encrypted, with a verifiable cryptographic signature of some sort.
I'm sure we all know the multitude of other attack vectors this introduces. I guess I am just not convinced that paper makes things more secure.