I doubt they’re part of a Mediterranean diet.
Looks more like Frankie Fishlips to me...
As their name suggests, deepwater tilefish are found at great depths, with some species found 600 m below the surface. They are important food fish, commonly found in seafood markets in East and Southeast Asia.
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The 250,000 Chinese fishing fleet should make short work of that species - later to be seen only in pictures.