Given that Baratheon blood works...
Baratheon is a branch from the Targaryens, with a refill only two generations removed from Robert, Stannis and Renly, so it might be that. And as TMSaxon said Melisandre has never really done anything with king's blood.
Also, though it can't be proven definitely yet, I generally get the feeling that Melisandre is consistently misinterpreting... Well, everything, so the odds of her actually getting something right seems low. Her character basically exists to do everything wrong so we can sit and scream at her and point to Daenerys (bloody stone dragons, right...)
and Jon
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