You are correct, based on what I have heard from a friend who tried to buy from Kesselrings. In the U.S., foreigners are not allowed to buy or transport firearms, parts, ammo or reloading components. {Police will not stop foreigners and search ther cars for these items but if they see them in a search incidental to another event, say you are involved in a vehicular accident or traffic violation, then you are out of luck. You have broken the law. At least that is what I have been told.
You may find a store that will sell you the stock, but that may be because they are not familiar with U.S. laws.
Canada Customs will not allow the same into Canada. Scopes may be a gray area because I have had red dot sights mailed to me from the U.S. Took 6 weeks because according to the ebay seller, the scopes have to be verified that they are not "parts", at a firearms center. Stocks are definitely firearms parts, not an accessory.