Fantasy Religion?

I have never been convinced by advice that when building a D&D-esque game world, a Referee should model their fantasy religions on those in the real world. Sure, draw on them for inspiration and motifs, etc. But when a D&D-esque fantasy world have a multitude of very real gods (or Immortals), each granting countless miracles each day to their priests, I wonder what room there is for some of the *best* bits of real world religion.

Well, it is a *best* bit when it is a fantasy world and you are hundreds of years removed...

In particular, what room is there for the corrupt priest? Or the secret heretic?

Of course, in a fantasy game world in which the gods are distant and inactive there is room for secret heretical cults with a church and worldly priests who abuse their robes. And distant, inactive gods are one answer, but they're not the answer for the assumed D&D game world. If the gods are active, intervening in human life, if there are unmistakable signs of divine favour (spells, for instance), these sinners and unbelievers will struggle to masquerade as blessed members of the church of the god who they offend.

Note: In Hammerstein!, my own game world (even though we're currently exploring Titan again), I have tried to give the schisms and heresies that are so interesting in real life (at least when you are removed by several hundred years) a fantasy analogue by having humans reject the 'Gods' (a race a cosmic superhuman beings) and instead worship 'Saints'. These are something like the Immortals of Mentzer D&D - humans who, by great deeds, magic, or the veneration of a community, have achieved some kind of intercessionary afterlife. This means that there are a multitude of Saints, some worshipped across the known world, others, such as the heroic ancestors of a single tribe, unknown beyond a single valley or town. This allows me as the Referee to create an endless number of [not-]gods, each with overlapping portfolios and rival interests. It also allows me to plug in all manner of localised real world pantheons by recasting them as heroic ancestors. At the same time - as they reject the Gods - they are all nominally part of the (Lawful) Church of Man, a civilising, unifying project that has a number of rival anti-popes. This gives me room for 'internal' religious conflicts that can range from bloodless doctrinal disputes (hopefully something more 'adventuresome' than to which of the competing Saints should the cobblers of Byzantium offer their devotion) to priests wading in gore as nations clash in war, rallying under the ikons and relics of their heroic ancestors. 

Anyway, do you have corrupt priests and heresies in your game? And what does their (watchful) god do about the bastards?