First off, the Church has never denied that “the body didn’t rot” isn’t the same as “incorruptibility.” Grace builds upon nature, and there are natural ways that you can keep a body from rotting. Alexander the Great’s body was once on display in a coffin full of honey, for example. For hundreds of years, it was one of the famous sightseeing spots of Alexandria.
However, when people say that a body is incorruptible, they are talking about something other than natural mummification or heavy use of embalming spices. If you are interested, you can look up individual descriptions of incorruptible bodies, many of them written up by guys who did undertaking and exhumation for a living. It’s not normal for a dead body, even one that just died, to look like a person is just sleeping. It’s not normal to have color in the skin instead of whiteness (lividity) or the dark red bruised look of blood settling. Once you get to someone who’s fifteen hundred years dead, the awesomeness of a coffin and a burial area don’t really help.
In Cecilia’s case, she was originally buried (for a couple hundred years) in a niche in the catacombs in her nice skinny cypress box. Plenty of other people were also buried in the catacombs in nice cypress boxes, but they weren’t found incorruptible.
Then she was moved by Pope Paschal to a safer spot inside the city, because of the invasions and disorder. At that time, her coffin was opened, so she was exposed to air again, and her coffin was moved through areas with more heat and humidity than in the catacombs. New silk was placed in her coffin, which should have brought along new micro-organisms.
But over the next thousand years, she still didn’t rot, or get covered with spores and micro-organisms from dust, as naturally mummified corpses easily have happen to them. (Witness what happened to the Iceman, or to many of the Peruvian and Chinese natural mummies. And they were in nice cold clean labs, for goodness’ sake!) Nobody describing the body described it in a mummyish way, either.
If you want to read what the finders actually said, here’s a translation of
Gueranger’s Life of St. Cecilia, with accounts by the historian Baronius and others. (Albeit it’s Italian or Latin, translated into French, translated into English. But it’s closer to a real source than me just talking about stuff.) You’ll have to shift around a bit to find the whole story and all the accounts, but Gueranger’s footnotes are there; and some primary sources might be digitized and online these days.
Similarly, when people talk about the “odor of sanctity,” they aren’t talking about any sort of ordinary perfumed smell (or the smell of death, or the smell of unwashed bodies, both of which get mentioned sarcastically by folks like Twain). Myrrh, frankincense, and other embalming spice ingredients were in common use in medieval and Renaissance Europe, both in medicines and in incense for churches. Nobody was going to mistake their expensive but common smell for something unearthly - and particularly not a priest! (And actually, the “odor of sanctity” is notorious for not being able to be smelled by everyone in the same place at the same time, for being smelled in different places in ways not compatible with air currents, for being compared to all sorts of different things or no known smell at all, and basically being much more the supernatural nasal equivalent of a vision than a natural odor.)
Incorruptibility was never classified as a requirement or definite sign of sainthood by the Church, east or west. In the West, it is generally seen as being a miraculous sign that often accompanies sainthood, because our bodies are transformed by life in Christ much as our souls are. It does tend to happen more often to ascetics, possibly because they work more on making their bodies Christ-like. However, it was well-known that St. Thomas Aquinas’ body was found incorruptible several years after his death, and he wasn’t known for starving himself or extreme asceticism.
In the East, there are several Greek islands where dead bodies are unable to decompose well, and the results are not pretty. Therefore, they try not to have cemeteries in such places. In folklore, the local people feel that anybody unlucky enough to be buried in such places is possibly cursed by demons or may even be a vampire. So yeah, natural non-rotting is not all fun and games, nor do people necessarily like it much.
If you are really interested, the future Pope Benedict XIV wrote a big huge multi-volume book on various miraculous phenomena, back in the 17th century. He was writing in a time of science, and he was the guy who ended up implementing the rules on how to determine whether an occurrence counted as an official miracle or not (largely by focusing on things that could be scientifically tested, since many miracles are more subjective and private than public and testable). But he did do a lot of research on what various miracle terms actually meant and what was actually on record about them from eyewitnesses; and you can go from there to more recent works.
Remember, most skeptic sites (like most religious sites) are run by hobbyists, or by enthusiastic people copying off what they read somewhere else. Very seldom do you find people appreciating the complexity of a subject, because they just can’t do it full time.
