I'd say this is a case of ambiguity on the English side. Consider, you and I both talked to Mary yesterday. You tell me, "Mary wants to go to Bali". I might respond, "Oh, that's interesting, she told me she wanted to go to Tibet."
In English, because we have two ways of reporting what someone says (direct and indirect speech) there's ambiguity that enters in the tenses. (Japanese doesn't have this distinction.) For English, depending on the context, both "she said she wants to go" and "she said she wanted to go" could both mean the same thing. (as in the scenario above). Nevertheless, without context, the second one sounds like she may have changed her mind.
But in Japanese, if you wrote/said
then this sounds like, "Mary said she had wanted to go to Tibet." But she's now subsequently changed her mind.
So, in Japanese, if you want to say "Mary said she wants to go to Japan", then you would say
Moral of the story, tense matters get very confused between English and Japanese.