The details of the crime seem to point to something like this.
Remember that Picasso was questioned and probably involved. One theory is that what we think is the original is, in fact, a master-copy by Picasso. The original is held privately in Florence.
He said the thief returned the original. The copies would have (supposedly) sold to people who wouldn't be able to complain without incriminating themselves.
There's a reason why you have connoisseurs. You can fool carbon dating by using materials from that time. I'll have to look into the x-rays and what they show, but it can be quite hard to prove art authentic with scientific methods alone.
They wouldn’t be able to do much with an oil painting. Any old drying oil from that time period would have long ago polymerized and carbon isotopes in any new oil used to mix the pigments would be a dead giveaway.
Remember that Picasso was questioned and probably involved. One theory is that what we think is the original is, in fact, a master-copy by Picasso. The original is held privately in Florence.