The Country of Origin stickers and tags need only accompany the goods into the US. They can then be discarded before the items are sold or distributed. Plenty of products do not show the country of origin at the retail and wholesale levels for this very reason.
It's illegal in the US to re-label products from another country as Made in America, or some similar falsehood. But it still happens a great deal, more than consumers will ever know. The practice is rampant in Europe as well, in particular Italy and Germany, where high-end goods are produced by Asian sources and then relabeled as originating from European countries.
My experience is mostly limited to leather products, such as hand bags and belts and such. However, the practice of false labeling occurs in countless other industries as well.