The argument that ANY firearm permit issued by ANY state is good enough to exempt a person from the GFSZ act is based on a couple of things.
Here is the subject part of the GFSZ act:
"(ii) if the individual possessing the firearm is licensed to do so by the State in which the school zone is located or a political subdivision of the State, and the law of the State or political subdivision requires that, before an individual obtains such a license, the law enforcement authorities of the State or political subdivision verify that the individual is qualified under law to receive the license;"
What some argue is that when a state passes a law that either recognizes another state or local permit or allows the "law enforcement authorities" to enter into an agreement with another state, they are issuing a "license" to that individual to possess a friearm in the state.
Key here is the term "license".
It does not mean it needs to be a document issued by the state. The state can issue a blanket "license" if it desires.
Since the state requires the individual possess a permit from another state or local jusrisdiction in order to be covered under the "license", this ensures that the individual has, in fact, been determined to be qualified under law to possess a firearm.
Another point that is argued is that from the federal perspective, they have a constitutional burden to give equal protection to all.
If an individual has been checked out and found to be qualified under law to receive a PA permit, they are under this statute, absolutely exempt from the GFSZ act.
In order to provide that individual with equal protection, they would have to be exempt in MO, even with a PA permit since the individual was in fact determined to be allowed to have a firearm.
While the state of MO could deny someone from PA the right to be near a MO school with a gun, while allowing a MO person with a gun to be there, the federal government can't do that - due to the US Constitution's 14th amendment.
Another point is that while one state may require a more extensive background check than another, the federal statute doesn't specify what the check must consist of.
The only reasonable check as far as the federal government is concerned would have to be the same information used for a NICS check. Since every place that issues permits in the USA does at least this minimal check, MO's recognition law is consistent with this.