If I recall correctly, objects with plural subjects work differently in Spanish and in English. In English, if there are multiple objects overall, it's plural. In Spanish, if there's exactly one object per subject, it's singular.
A translation that gets the sense of "Ellos tienen una camisa", if I'm remembering the difference right, is "They have a shirt each." On the other hand, "They have shirts" could be translated with either "unas camisas" or "una camisa".
I guess I'm wondering how much of this Duolingo accepts, given that I did a word-for-word translation into a sentence that doesn't quite make sense, but was accepted.