I can see her point - 'sharing' is facebook jargon and when you 'share' a 'facebook photo' publicly, the symbol next to the picture used to represent the public or 'global' share is one of the earth - and as dejongj says, the original source would be seen by all facebook users seeing the shared picture. "Share with the world" and "displayed to all our fans" is not the sort of phrasing that I would expect a company to use when asking for the use of a photo for advertising purposes - and given the context (the picture on facebook and the request by Miller via facebook messenger), I find it dubious that Miller didn't put some thought into how they worded their request - no mention of TV or any other media; the use of the word 'fans' to describe what turns out to be not fans but television viewers (remember, facebook users can 'like' company/product pages if they are a fan).
But saying that, I would expect someone with her credentials to have enough nous to be suspicious and ask questions before giving her permission.