The thing that was impossible was him being able to have 2 fruits at once, and is probably specific to Blackbeard himself.
It was shown when Smiley died. An apple that was laying nearby transformed into his Devil Fruit.
So Blackbeard likely just killed Whitebeard while having a fruit on his person, and when it turned into the Quake Fruit, did...whatever he does that allows him to eat another fruit while already having one.