Not a tax expert, but....
If you pay a guy in another state for a gun, The sale occurs in that state, not yours.
The seller most likely is not going to collect taxes.
Once the gun has been bought by you in the other state, it is your gun.
So when you ship it to the FFL it is already your gun and no sales tax is due.
The issue is that no tax was collected anywhere for the sale, so your home state wants to hit you with a "use" tax. All states are looking for money anywhere they can get it. The interstate commerce protection act clearly states that no taxes are collected on sales that occur across state lines. The exception is for business that have a presence in more then one state. They must collect in all states that they are in regardless of shipping point.
However,, that being said you are still be obligated to pay the "use " tax on the item. States have only just begun to explore charging this use tax as the volume of out of state sales has drastically increased with the advent of Amazon,etc.
So yes you are to report and pay the tax.
Pennsylvania sends out an official request to list all internet purchases and the tax due in an attempt to collect.
It is the burden of the state to prove you made the purchase and owe the tax. The form is a voluntary admission of owing taxes.