The French commonly use the verb prendre to mean to have when it comes to food and drink. While DL's translation is correct, it's a bit odd. Had fish and had some fish are better translations, but are not accepted.
Maybe in a conversation after eating it could infer that the person has eaten the fish, but that's not enough to make it a correct translation. I'm thinking of a situation where there is a buffet and you chose to get some fish. "I ate some fish" - J'ai mangé du poisson.
I think you are probably right that this is what you would say at a buffet. Most English speakers would probably say "I had some fish" meaning that they took some fish. Duolingo didn't accept my "had" though.
Forgive me, Germandy, but in my experience in the UK one should say 'it could be inferred that the person has eaten the fish'. Or, did you mean, to say 'it could imply' that they had? That would be more correct, as well as less wordy.
Parce que la phrase est hors de son contexte elle peut avoir plusieurs traductions. Traduire "I took some fish." avec "J'ai commandé du poisson." devrait être acceptable même si la traduction mot-à-mot serait plutôt "j'ai pris du poisson."