fiddletown is actually speaking about a separate issue. His response is correct, just not applicable to the subject of the thread, nor applicable to okiefarmer's sidenote...
In other words, right answer but to the wrong question.
1. An individual may ship a handgun to an FFL in any state.
2. An individual may ship a handgun to himself, for sporitng purposes, in another state.
3. An individual may ship a handgun to a licensed gunsmith or the manufacturer in any state, and the gunsmith or manufacturer may return that handgun directly to the same individual in any state.
4. A private party may not conduct a transfer of ownership with an out of state resident without going through an FFL in the recipient's state of residence. How the handgun gets to that FFL is not specified in the Federal Law.
#4 above is the statement that fiddletown made, which is correct, it just wasn't an answer to any question asked.
Now, for the OP's question. Some FFL's will not receive handgun shipments from private parties strictly as a CYA measure. If the recipient, for instance, does not pass the background check and cannot take possession of the handgun, the FFL cannot send that gun back to the sender out-of-state. It would have to go back to an FFL in the sender's state of residence for transfer back to the sender.
If the sender does not include a copy of their own ID with the handgun, the receiving FFL could not properly document receipt of the handgun.
It is NOT a matter of potentially receiving stolen goods, because the FFL receiving the handgun, whether it comes from another FFL or from a private party has exactly the same resources available to check if the handgun is stolen or not - so that is not changed by who he receives the handgun from.