Probably. Practices tend to differ from company to company, but in general many big corporations retain employee files for HR to reference should they try to come back.

I was about to hire a girl at my last job, but then HR told me they were ineligible for rehire by the company, I believe for time-theft by manipulating the punch clock. It was a shame because I really coulda used an employee with her skills, but maybe it was for the best

I don’t think they have blacklisted you, but your history with them could be the deciding factor when they have other candidates to choose from.

I really doubt their computer systems are that smart

Fact ... I am sure they are not that smart