Um, MechAG, most names (particularly those of people who are going to be questioned about illegal status) are fairly common. This means that people are going to be flagged incorrectly, one way or the other. If you're an illegal, why not just guess a random, common name that's going to come up as 'legal' and walk away? If we open that system up, such that the cops might not believe you and can detain you anyway... we're back to square one.
In this case, people are being detained already and the immigration status check has been added to the standard "open warrants" check. They are not yanking people off the streets to check papers. That is a hypothetical situation that has been added to this conversation.
Fake names were a problem last year and will be next year, regardless of this change. Since we are talking about people who are already being arrested and likely fingerprinted, I am not sure it changes anything.
I agree that if someone is not being arrested/detained for some other reason, he shouldn't be detained for any extra immigration checks or ID checks. I agree the potential situation could be bad, but I just don't see this situation as moving that direction.