I think that's because in English, when you want to state a known fact like that one, you should not use the definite article. Instead, you would say "Dogs don't eat birds". So, in my opinion there's no ambiguity in this sentence – it can only be translated as: "The dogs are not eating the birds."
This question is not really about this question but in general, its just that in general how can you dofferenciate in Norsk the difference between a general statement like "The dogs eat food" ("Hundene spiser mat") and present statements lile happening in the present "The dogs are eating food" because this causes a big deal of confusion in spoken language, no?
The way I see it, saying "They eat meat" can mean either that they eat meat in general, or that they are currently eating meat, whereas saying "They are eating meat" can only mean that they are eating meat at the moment. The same thing happens in the German course. If I am wrong, please feel free to correct me!