I can see that.
I'm sure that they could design a system that actually records our individual votes, but then we'd have that old "secret ballot" issue.
Actually, there are cryptographic protocols that handle this rather well. You can have secret ballots where the eligibility of the voter is verified, the vote can be verified (i.e., it's auditable), and each individual vote is verifiable. Bruce Schneier wrote about it in Applied Cryptography. The problem is that any system that satisfies all three requirements, (verification, auditability, secrecy), is pretty darn complex. I cannot imagine having enough trust in the government that they could pull off such a complex thing successfully without having at least one of the thre requirements be violated.