I believe the issue is coming back to the US and not leaving the US - the TSA wants the documents to bring your rifle back into the US. I am happy to see people taking suppressors to Africa then back into the US. I was told that TSA would impound the US citizen owned suppressor upon reentry into the US. Adding it as a line item on the ATF document must be the ticket.
Exactly. The form is the only proof that they accept that you bought it here and took it out of the country - and that you didn't buy it out of the country and try to sneak it in. I think a simple 4457 form would have covered you with the suppressor.
For all of you readers considering traveling out of the country to hunt, you need to be VERY aware of this, from the cbp.gov site:
"Hunters who plan to travel with their licensed firearms must obtain a
Customs and Border Protection Form 4457, Certificate of Registration for Personal Effects Taken Abroad. This form provides the traveler with a document that lists articles that will be taken out of the country so they won't be charged duties on these items upon return to the United States. This form is in addition to any import, export, or sportsman's licenses that may be required in the destination country.
"This form allows a CBP officer to verify that the traveler has that property in their possession while they're exiting the United States," Ehrlich explained."
Also know that this form will cover you for expensive watches, jewelry, cameras and other high value items. They profile actively for this type of stuff. It's also a felony if you get caught actually lying on the form.
It's also a pain to execute the form, since you have to present the items for listing on the form to CBP before you leave. This way you can't create the declaration - and then buy the item outside of the country and try to cover it with the form. Cute - eh??