As a German who lives on the danish border, i might shed some light on that. "Rugbrød" actually is (mostly) made from rye. It usually is a very dark, sourdough like bread, usually with the grain not being completely ground. Google for pictures...
German "Roggenbrot" however is a bread made mainly of rye, but ground. It may or may not be the sourdough type, depending chiefly on the wheat content. We also have the equivalent to the danish "rugbrød", which we call "Schwarzbrot", literally "black bread".
And the idea of danish "rugbrød" being exported....well...certainly not to Germany! ;)