I think a lawyer could successfully argue that it should be accepted. But I also think common sense would argue that you would need a specific context for the sentence to mean that. Without the context, 'su' naturally refers to the person that was mentioned earlier in the sentence.
Su cuna. Su is used for anyone that can use a 3rd person singular or plural verb. So, technically, his, her, your (usted, ustedes), their. But without context, we should probably see it as referring to the boy, who is the subject.
I'm not comfortable, though, that Duo didn't give you the preferred answer as your correction. There's no reason to give you her when his is the answer they're showing on this page.
Because "may be" (always the context) the boy isn't in HIS cradle, but in other baby's cradle who happens to be a girl. Or the boy is not in his house, and now is sleeping in the cradle of her (the friend of his mother) or in THEIR cradle (the friends of his mother)... many different possibilities here...