I recently came across a theory on Tower of the Hand that speculated that Daenerys may not be a Targaryen at all, based on the cryptic messages of Quaithe to “remember who you are” and implying that her memories of the red door in Braavos aren’t the memories she believes them to be. I didn’t buy the suggestion that she might actually be the daughter of Ned Stark and Ashara Dayne, but the possibility that she’s a previously hidden Blackfyre doesn’t sound implausible. What are your thoughts?

No. Dany is Daenerys Targaryen, daughter of Aerys II and Rhaella Targaryen. Her birth was witnessed by servants, bannermen, and Viserys; it happened while the island was under naval blockade so there was no smuggling anyone in (it took the storm of a century to allow Ser Willem Darry to sneak through). 

On a metatexual level, GRRM is not M. Night Shyamalan, he doesn’t do twists out of nowhere or for no reason – if you go back to GRRM’s texts, he very carefully layers in huge amounts of foreshadowing in ways that make things super-obvious when you do a re-read. So if he wants a character’s identity to be open to question, as with Jon Snow, he puts in a huge amount of material pointing in that direction.

He didn’t do that with Dany. He did the opposite, repeatedly tying her back to House Targaryen. AGOT and ACOK are filled with references to Rhaegar, Aerys, prophetic visions of Rhaegar and Aerys, and so on and so forth.