Not true.
A product assembled in the US with foreign made parts can not be labeled Made In The USA if those foreign parts make a non-negligible portion of the finished product.
2 examples given at the site below are:A grill assembled in the US, with a US made shell, burners and controls valves but with knobs from Mexico can be labeled as Made In The USA since the knobs are insignificant to the overall product.
A lamp assembled in the US, where the shade and brass are US made, but the base is imported can not be labeled as Made In The USA because the base is a significant part of the lamp. It can be labeled as "Made in U.S. from Imported Parts" or "Assembled in USA" but not labeled as simply Made In The USA.