[Antoninus]

While this is the first (and so far only) mention of King David outside of the Bible, it does not exactly prove his existence nor the historical role assigned to him by the biblical texts.

It doesn't prove it. However, it does provide very strong evidence for it. With archaeology, circumstantial evidence is generally the best you can do, and as circumstantial evidence goes, this is a lot stronger than most of the other claims put forward on the program.

[VietVet]

Correct. While it does not prove the existence of David the King of a united Kingdom of Isreal and Judea, as an important political figure in his own day, it does prove that, about a century after his own time, his memory and the tradition of his reign was important enough in Isreal for a current King to claim him as an ancestor.

Better proof would be contemporary documents or monuments, from Isreal, Judea, Philistine, Syria, Phoenicia, Mesopotamia, or Egypt recording his name and office.

If this was the among the stronger pieces of evidence presented, a skeptic would say that the show did not make a very good case for whatever it was trying to prove.

VietVet