"Do Employers legally have this much power over AT-WILL employees"
Yes. The employer can require employees to be fingerprinted for this reason and it's legal.
Why would they not consent to it unless they had something to hide?
A non-chattel state has nothing to do with this.
If it were me I would have given them the fingerprint. They must be going to a biometric access time system. It isn't that big of a deal. I just got back from a MAJOR theme park and when you use one of their multipark tickets or a yearly pass you have to have your finger scanned at every gate to use it. It keeps people from re-selling their unused portions of the tickets as well as protecting against stolen tickets and passes.
Whether or not they get UI benefits will be decided by the state. The employer can protest/fight it all they want but if the state awards benefits it's a done deal. If they are denied benefits the employee can appeal.
"That's just my opinion, then again I might be wrong." Dennis Miller