I doubt that what is said is true. Even if the carving did moisten before a Pope's death, God could be working through the carving. But like I said, I am very doubtful as most "supernatural" occurances turn out not to be supernatural after all.
If you ever are in Western Europe, check out some displays of incorrupt saints. God has shown His approval of these saints by preserving their bodies from decay. Most of them were buried in simple wooden caskets and with little to no embalming (but not all of them as Pope John XXIII was buried in a triple sealed air tight container). Even if you are not Catholic, it is something I hope you will check out.
I saw some bodies on display in the Vatican... I was repulsed, for obvious reasons. I fail to see how faith is supported by the display of human corpses.