As a Swiss, I can assure you that this is false. Most cheese varieties have very strict quality requirements, if they're not met, the cheese may only end up as no-name ground cheese for pizza or something like that. But an Emmentaler, Gruyere, or Sbrinz always has the same quality, no matter if it's exported or for domestic consumption.

As a Frenchman I disagree, cheese is very sensitive to environmental condition, in particular during transport. To eat a good piece of St Nectaire, first go to to St Nectaire (eat the crust too!)

As an American living in CH, I say send all of the (bland) Emmentaler to the U.S.; I wouldn't miss it! ;-) Inländervorrang for the rest!