Stop in for a cup of coffee

Why would you feel bad? Their internal issues are not your problem. If what you were told is the true story, that guy probably left hundreds of cars out with unbalance, unsafe tires. That doesn't explain why the old tire was still in inventory for a rookie to accidentally use it. Or why nobody was checking his work. I doubt he files his own paperwork. Probably goes to someone in the office for billing.
That's why the assistant manager got demoted, it's his job to rotate and verify tire dates and safety. It's also his job to file all paper work and to verify the work was done.