Who told you that? What policy, rule or law was the basis for that opinion? What authority exists to make that policy, rule or law valid?
The gun laws are a little muddled in MO. I would guess that the Airport is relying on this state law:
RSMo 571.107.1.(6)
(6) The general assembly, supreme court, county or municipality may by rule, administrative regulation, or ordinance prohibit or limit the carrying of concealed firearms by endorsement holders in that portion of a building owned, leased or controlled by that unit of government. Any portion of a building in which the carrying of concealed firearms is prohibited or limited shall be clearly identified by signs posted at the entrance to the restricted area. The statute, rule or ordinance shall exempt any building used for public housing by private persons, highways or rest areas, firing ranges, and private dwellings owned, leased, or controlled by that unit of government from any restriction on the carrying or possession of a firearm. The statute, rule or ordinance shall not specify any criminal penalty for its violation but may specify that persons violating the statute, rule or ordinance may be denied entrance to the building, ordered to leave the building and if employees of the unit of government, be subjected to disciplinary measures for violation of the provisions of the statute, rule or ordinance. The provisions of this subdivision shall not apply to any other unit of government;
http://www.moga.mo.gov/statutes/c500-599/5710000107.htm
This may or may not apply to open carrying. It's not been tried as far as I know, and I'm not willing to be a test case, even though I have my CCW endorsement.
Edit: the gun laws are muddled in MO, not KCMO, KCMO is perfectly clear with respect to their laws.