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I've done some thinking on this myself, because I love fossil Pokémon. All of them from Kanto and a couple from Hoenn are some of my favorites.
Simple logic would lead you to believe that over the millennia the DNA which is extracted to revive fossil Pokémon has been infused with the rock that surrounded it. In other words, Omanyte and Kabuto may have been pure water before they went extinct, but the process of fossilization caused their types to change in accordance with their rocky prisons.
Coincidentally, however, this theory prevails over every other except in the case of the Pokémon you posted--coincidentally the best fossil Pokémon--Aerodactyl.
Aerodactyl are revived not from sediment, but rather a piece of Old Amber (which I'm assuming encases only a portion of the Pokémon; maybe a wing or scale.) There is no rock in plant matter, and if we follow our original line of thinking it should be clear that Aerodactyl would have absorbed the Grass type making it Grass/Flying.
This is obviously not he case, leading one to throw out the textbook and assume either A) Aerodactyl was a Rock/Flying type and did not go through the same transfer process as the rest of the fossil Pokémon, adopting the type after revival, B) All fossil Pokémon just so happen to be rock types, or C) the Old Amber literally hardened the DNA to the point where the process metaphorically and thematically transforms revived Aerodactyl into the rock type whereas it was originally only flying.
My money's on C, but the actual answer is the Old Amber is just a Jurassic Park reference and they weren't thinking about it.
Hope that helps!
