On our end, the only controlled import item is the receiver. Our government has no restrictions on the other firearm parts.
Our government has some restrictions on other firearms parts. We had excitement locally when it was discovered an importer had some AK47-type drum magazines that were supposedly made in Europe but actually made in China. I think there's German fella in our federal prison now.
It's either legal to ship a gun barrel or it's not. Calling an illegal item by another name isn't a wise move.