Well based on the link you provided from the Catholic News Agency, it looks like Kim Davis or her spokesperson is not giving the right impression to the public.
Since according to your link :
... the Pope “did not enter into the details” of her situation, and specified that the meeting with her “should not be considered a form of support of her position in all of its particular and complex aspects.”
Then, the reports about the Pope telling Kim Davis to “stay strong” might have come from Davis herself. Which seems to be a false impression she is trying to give.