Whoever told you the information I have put in red is full of it. You can mail it ordinary first class mail if you want to.
The requirements for mailing a firearm are clearly set out in the Domestic Mail Manual (DMM) which is in every post office in the United States and online.
Also, footnote, federal gov't does not consider BP guns to be "firearms" (go figure) so you can send a BP pistol through the mail.
