DK, you are right that once the ammo is in the States, you can buy it without a Form 6 or any kind of Permit.
The person who RECEIVES the ammo in the US must have either a Form 6 for private import or be an commercial importer with all the required for that. The Form 6, and the permits for commercial import are required for either guns or ammo and that is how the regulations are written. A few years ago, there was a cartridge collector/dealer who had an commercial import permit and use to bring in both guns and ammo, but mostly from Canada because that was much easier than bringing things directly from Europe. There are restrictions based on “prohibited countries” so ammo from Albania and North Korea cannot be imported.
If a package of ammunition is shipped from overseas, and properly marked as live ammunition, Customs will hold it and will not release it to you until you present an import permit. Then there is a green form that is signed by Customs that shows what you actually imported and you have to send that back to the ATF.
The option is not to mark the package as live ammunition, which will work, but is not legal and with the way material is screened these days is a very high risk, and a very very bad idea in my opinion.
The only exception to this I know of is for very old ammo in some long obsolute calibers. One IAA member who regularly goes to the ECRA meeting sent in his Form 6 application and got back a letter telling him that no permit was required for these old and obsolute calibers (all very old rimfires I believe).
Hope this helps.