"She [the mother] used to say that she [the daughter] was a girl" - now she [the mother] acknowledges that she [the daughter] is grown up.
"She used to say that she was a girl" - in order to clarify when people misgendered her; now she just lets people assume she's a boy if they will
"She used to say that she was a girl" - now she says that she's a woman
"She used to say that she was a girl" - even until she was 90
Seriously, the problem is not with Duolingo; the problem is with your imagination :p
"She said that she was a girl" was accepted, but it also offered "She used to say that she was a girl" as a variant.
One refers to a one time occurrence, another to a habit.
Is one of them a more correct translation, or is exact meaning supposed to be inferred from context with that kind of phrase? Is there a way, when I say something like that, to clarify if I mean something that happened once or something that used to happen regularly?
I translated this as She was saying that she was a girl. It is difficult because when I see imperfect I think of a recent past. Used to (to me) sounds like a distant past. My friend in Mexico says that ''used to'' is ''solía,'' but sometimes it can be imperfect. I guess I just need to know when imperfect = used to. Every time I think I understand, I get sentences like this one.
I think the DL sentence is made complicated by an unusual idea and a complete lack of context. If it said, "She always used to say that, in her youth, she was as beautiful as Greta Garbo." it's an easy sentence. The first part is indeed a continuing state of affairs - a belief that was expressed throughout her lifetime. The second part is how she looked at a particular time, so preterite. I see a lot of sentences like this, that express the past in both ways. "She vacuumed the house every Saturday until she died." The vacuuming was an ongoing event, the dying was a singular event. A few extra words in the DL sentences would certainly make all this a little easier. :)