Why do you trust any OK certified food then?
What's the difference if it's packaged in a warehouse in FL or served in a restaurant in FL?
What it comes down to is who is actually responsible for the food your eating.
According to many in the kashrus business the OK has good policies and supervision when it comes to factories that they supervise.
However they have been known to put blind trust in ppl locally to set thier own standards in regards to policies and supervision for local hashgacha.
Look at it like a franchise. If you trust the local rabbi in charge of the local OK branch then your good to go. If not you can still trust the flagship to be reliable in regards to the standards he is in control of non local branches.