I see what you mean. The sentences have the same meaning, but the style is different, which is why they won't accept that. I would translate "He eats lots of Danish pastries" to "Han spiser masser af wienerbrød." It sounds slightly more colloquial to me. Hopefully a native speaker can chime in here though :)
actually wienerbrød is a "bread" or a sort of pastry made with puff pastry. The austrians have introduced it in Europe. Marie-Antoinette brought it in France in the 18th century as she married Louis XVI before the revolution. What is typically French now the socalled "Croissant" is actually Austrian originally. Wienerbrød i Denmark smager rigtigt godt
Additionally, the dough itself is called the "mille feuille": a thousand layers in French <3 The croissant (meaning crescent in French )has an interesting myth around it too: It is said to have been created by the bakers of Vienna to celebrate the victory against the Ottoman Empire (whose flag has the crescent symbol). After the Ottoman army retreated from the gates of Vienna emptyhanded, the city celebrated with a party including this new pastry. I think history is sometimes hilarious and delicious.
Well, it doesn't mean any kind of pastry that comes from Denmark. Being named "Vienna bread" would be quite far off in that case.
It refers to any kind of fluffy doughy goodness that I think you collectively call "Danish" or "Danish pastry" in the US. Just do a google image search for wienerbrød to see what it refers to. Hold a napkin ready.