You are right about it being an Omaha city thing. I had a OPD cop tell me the only people who can carry openly in the city are people who have a 'need', ie security people, PI's, etc.
If I have to prove a need, then the question necessarily arises: "to whom?" Whomever has the power to recognize (or refuse to recognize) my need, becomes the one granting me the right. And that is precisely what the Constitution does NOT do.