A U.S. Company called Longines-Wittnauer (LeCoultre-Vacheron Constantin) was formed in the U.S. to market, case and time "LeCoultre" timepieces. Special attention was paid to U.S. market needs with the use of Gold Fill, 14k gold and less conservative case designs.
However, to say that this entity's relationship with JLC Switzerland was only limited to the supply of movements is simply not supported by the many watches that exist under both nameplates.
Hard evidence to the above can easily be found in U.S. market watches bearing the LeCoultre name which match up to their Swiss counter parts 100%, typically in steel & 18k. Also note that many Swiss market JLCs have "LeCoultre" signed cases bearing Swiss Hallmarks which are entirely correct.
So, yes, perhaps they were different legal entities but to make the claim that JLC only supplied movements to a company that has nothing to do with them, is not supported by the many hundreds of watches I have personally examined.
Here is a good example of the tight relationship of the 2 companies.