Where exactly is your evidence that the US government is behind this? From the evidence you present there does seem to be a case that this girl is being used for propaganda purposes. But where do you have any evidence that the US is behind this? It could be the Kurds, the Turks, anti-regime rebels, Sunni countries in the region or a dozen other actors.
It is pretty sloppy to accuse the US of backing this girl without evidence. Its the kind of thing Russian propagandists would love. Is that the perspective you want to be taking?