Is there a 'refutation', i.e. a defense for black that leads to a guaranteed advantage assuming perfect play, against the Muzio gambit?
[StartPly "11"] [FEN ""] 1.e4 e5 2.f4 exf4 3.Nf3 g5 4.Bc4 g4 5.O-O gxf3 6.Qxf3
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First of all, I should point out that it's actually simplest to avoid the Muzio altogether with Black; i.e. meeting 1 e4 e5 2 f4 exf4 3 Nf3 g5 4 Bc4 with 4...Bg7 (the Hanstein Variation) or 4...Nc6! (transposing to a line of the Bishop's Gambit which is probably favourable for Black.
But that doesn't really answer your question, does it? :)
After 1 e4 e5 2 f4 exf4 3 Nf3 g5 4 Bc4?! g4!? 5 0-0 gf 6 Qxf3 Qf6! 7 e5!, Black almost always plays 7...Qxe5, which has been analyzed for centuries, and the verdict is still unclear. However, in his recent book, John Shaw puts forth the view (supporting by the strongest engines) that 7...Qf5! leaves White with doubtful compensation for the piece.
Conclusion : 4...Nc6! and 4...Bg7 give Black good prospects to play for an edge in a relatively simple position (which is a good practical choice given the rarity with which Black meets this variation). Speaking about the Muzio proper, things are much less clear, but 7...Qf5 should be better for Black (albeit complicated).
After achieving the state of the 'Muzio Gambit', White has a very distinct advantage via development. But at that point, the advantage is firmly established: Anything that Black could've done to prevent such an egregious advantage would've prevented the board from reaching the defined 'Muzio Gambit'.
The only thing that could save Black at that point, is if White does not maintain constant attack pressure, and allows Black to develop.
I have never come across any technique that Black could do to regain control from a very aggressive White player.