Preemption laws and leases of public property:

Here's a legal question that combines some of the favorite topics at the VC. David Nelson is the head of Stonewall Shooting Sports, the pro-gun gay rights group in Utah. At the upcoming Utah Pride Festival, Nelson wishes to carry a firearm lawfully, as Utah law authorizes him to do. However, the festival operators (a private organization) have a rule against carrying firearms at the festival. The festival takes place on public property, which is leased by the festival operators. The Salt Lake City police provide security for the Utah Pride event, and enforce the organization's rules, including the gun ban.

Utah's firearms preemption law states:

63-98-102. Uniform firearm laws.
(1) The individual right to keep and bear arms being a constitutionally protected right under Article I, Section 6 of the Utah Constitution, the Legislature finds the need to provide uniform civil and criminal firearm laws throughout the state.
(2) Except as specifically provided by state law, a local authority or state entity may not:
(a) prohibit an individual from owning, possessing, purchasing, selling, transferring, transporting, or keeping a firearm at the individual's place of residence, property, business, or in any vehicle lawfully in the individual's possession or lawfully under the individual's control; or
(b) require an individual to have a permit or license to purchase, own, possess, transport, or keep a firearm.
(3) In conjunction with Title 76, Chapter 10, Part 5, Weapons, this section is uniformly applicable throughout this state and in all its political subdivisions and municipalities.
(4) All authority to regulate firearms is reserved to the state except where the Legislature specifically delegates responsibility to local authorities or state entities.
(5) Unless specifically authorized by the Legislature by statute, a local authority or state entity may not enact, establish, or enforce any ordinance, regulation, rule, or policy pertaining to firearms that in any way inhibits or restricts the possession or use of firearms on either public or private property.
(6) As used in this section:
(a) "firearm" has the same meaning as defined in Subsection 76-10-501(9); and
(b) "local authority or state entity" includes public school districts, public schools, and state institutions of higher education.
(7) Nothing in this section restricts or expands private property rights.
Utal has another preemption law. It says:
76-10-500. Uniform law.
(1) The individual right to keep and bear arms being a constitutionally protected right, the Legislature finds the need to provide uniform laws throughout the state. Except as specifically provided by state law, a citizen of the United States or a lawfully admitted alien shall not be:
(a) prohibited from owning, possessing, purchasing, selling, transferring, transporting, or keeping any firearm at his place of residence, property, business, or in any vehicle lawfully in his possession or lawfully under his control; or
(b) required to have a permit or license to purchase, own, possess, transport, or keep a firearm.
(2) This part is uniformly applicable throughout this state and in all its political subdivisions and municipalities. All authority to regulate firearms shall be reserved to the state except where the Legislature specifically delegates responsibility to local authorities or state entities. Unless specifically authorized by the Legislature by statute, a local authority or state entity may not enact or enforce any ordinance, regulation, or rule pertaining to firearms.
Nelson argues, inter alia, that subsections (4) and (5) of the first statute leave Salt Lake City without any authority to restrict the carrying of firearms, yet Salt Lake City, by leasing public property to a private organization which bans guns, and by using local police to enforce that ban, is doing so.

Does Nelson have a valid legal argument? Does (7) save the Utah Pride's ban? Answers which supply specific legal authority will receive the highest grades.