Early Christianity's Dirty Little Secret?

My good friend and Biblical scholar, Brian Schultz (Ph.D. Bar Ilan University), poses the following question about the Jesus-family-tomb hypothesis:

How could Christianity spread as a religion about a resurrected messiah when the entire Jerusalem community, including James, brother of Jesus and leader of the church, knew where Jesus' tomb could be found?

Good question. Brian is assuming, with good reason, that the location of any given family tomb would not be a secret. He continues:

Even discussing the possibility that this tomb could be of Jesus is an insult to the intelligence of 1st century people, both Christians who believed the message, and Jews who felt they had to fight against it without ever appealing to his existing tomb that continued to be in use for at least another generation!

The point is that as Jesus' family tomb, it would have been used and reused over the next generation, presumably up until 70 C.E. Is there any evidence anywhere that this location, or any location, was rumored to be the final resting place of Jesus? The closest we have, I suspect, are texts that hint at the possibility that the body was moved from somewhere else (Mt 28:13; Jn 20:2, 13, 15). Which isn't very close.

As Schultz reminds us, the Jesus-family-tomb hypothesis requires that this tomb be used by Jesus' family over several generations precisely when his family and others are proclaiming that Jesus' body did not stay in the grave. Personally, I find the idea that Jesus' family had a dirty little secret about as plausible as the idea that Mary Magdalene snuck off to France so her daughter could marry into the French royal bloodline.