A private entity can have whatever policy they want regarding guns. They don't fall under the definition of "public" regarding the weapons storage laws.
"Public" property is state and local government property. If you enter state or local government controlled property, the "operator" of that property has the option of banning weapons but must provide storage. Depsite the specifity of the storage requirements, it's ignored, and there is no penalty for them not following the law.
We (AzCDL) got HB 2729 through the legislature last year to fix that, but the governor vetoed it.
Gun shows usually ban loaded guns for safety (and probably liablity insurance) reasons. Too many people think there is a difference between a loaded gun and an "unloaded" gun when it comes to handling them