Produced by James Cameron and directed by Simcha Jacobovici, this program takes its viewers into one of the most productive fields of archaeology. Prior to the destruction of the Temple in 70 CE, the Jewish population of Jerusalem buried their dead in a distinctive way. Bodies were laid out for a year in burial caves. After that, their bones were either deposited in a common pit or, when wealth permitted and status demanded, gathered into a limestone box called an ossuary. At the time of transfer into this tiny coffin, the name of the deceased was sometimes scratched onto the side or back of the bone box.

In 1968, the ossuary and skeleton of a young man who had been crucified by the Romans was unearthed, complete with a nail driven into his heel. This discovery showed that the victims of crucifixion were not necessarily tossed to the dogs after their executions, as was commonly repeated since the end of the 19th century. It could be mean that Jesus was indeed buried in the tomb of Joseph of Arimathea. Another myth was laid to rest in 1990. It had been said that the Jewish opponents of Jesus in the Gospels were made up, and their names fabricated. But that year, the ossuary of Caiaphas, the Jewish high priest at the time Jesus was executed, was discovered at Abu Tor near Jerusalem.

“The Lost Tomb of Jesus” focuses on another burial cave found south of Abu Tor, at Talpiyot, in 1980. In the cave, several ossuaries with inscriptions were found. One of them probably states “Jesus, son of Joseph” in Aramaic. (I say “probably,” because there is dispute in deciphering the scrawled script and additional scratches in the first word.) Amos Kloner, the lead archaeologist at the time, catalogued and described the find. So why didn’t he call adequate attention to this discovery?

This question is the premise of the documentary, which argues that the Israel Antiquities Authority is afraid to admit that it has been keeping Jesus’s coffin in storage all these years. But in fact, the IAA did call attention to everything they found in the tomb, professionally and critically, and made a careful presentation of the results in published form.

Yet Simcha Jacobovici remains dissatisfied. He argues that a vital factor has been overlooked by archaeologists. Although both “Jesus” and “Joseph” were common names, and well represented in ossuaries, what about the statistical improbability of other names appearing with Jesus’s that are also associated with him in the Christian Bible? Simple math is explained repeatedly in the program: the observation that, although, say, “John” and “Jackie” and “Joseph” are all common names, the likelihood of finding them all in the same grave is remote, unless we are dealing with the Kennedy family.

In some ways, Mr. Jacobovici, who also shared the writing credit, rises to his own challenge, placing himself in the role of intrepid archaeologist and investigative reporter, bravely struggling against the bureaucrats of the IAA. Mr. Jacobovici, who presents his rhetoric as a carefully crafted case, has clearly learned much from Mr. Cameron, the director of blockbusters like “Titanic” and “Terminator.”

The climax of Mr. Jacobovici’s argument is that Jesus was buried in the cave with Mary Magdalene, that she was his wife, and that their child is buried along with them. By pressing into that conclusion in a relentless rhythm, Mr. Jacobovici bypasses some basic questions. For example, if Jesus’s followers actually had enough money to buy a lavish mausoleum, why did they mark his tomb as “Jesus, son of Joseph”? After all, the earliest writings in the Christian Bible show they referred to him in Aramaic as “Lord,” “Messiah,” and “Son of God.”

In a world of special effects, we are accustomed to sliding past these and other issues. The key special effect, however, poses a problem for the program. The simple fact of the matter is that the name of Mary Magdalene does not appear on any ossuary in this alleged Jesus family tomb. Instead, a Greek form of the name Mary (in the Greek alphabet, not Aramaic) shows up, a form affected by wealthy ladies in Jerusalem whose families could afford ossuary interment. The evidence of this name suggests that the tomb is in fact not the last resting place of Galilean peasants, but the mausoleum of an aristocratic family in Jerusalem with pretensions to Hellenistic culture.

Mr. Jacobovici has somehow turned this rich dowager into Jesus’s svelte wife (as she appears in the program’s re-enactments). He pulls in Harvard professor François Bovon, who says — quite rightly — that in a 14th-century copy of a fourth-century text the Greek name “Mariamne” might be a reference to Mary Magdalene. That, of course, is completely beside the point. Did Mr. Bovon know that he would be quoted to make a claim from such late sources about a first-century ossuary? He seems uneasy in the interview, and the result shows he had good reason to be worried. In the end, he served as the stunt double in a special effect that did not come off, and his unease signals the alert viewer to the weak thinking behind the program.

Ossuaries will no doubt continue to illuminate the events and setting of first-century Jerusalem, including Jesus’s last days in the city. Viewers of this program might well enjoy it as an introduction to the topic, as well as a caution against trying to arrange facts into convenient shapes, even with the blessing of statistics.

Mr. Chilton’s biographies, “Rabbi Jesus” and “Mary Magdalene,” are available from Doubleday.