Divine intervention can happen, but as you pointed out, it requires confirmation by the church to become part of canon (and, as such, recognized as an actual intervention by the divine). However, it is typically much more frequent in fantasy worlds because gods often manifest in much more tangible and direct ways and people are fairly open to the idea that the gods have a hand in their lives. Historically, polytheistic religions had a similar outlook on divine intervention: the gods were 'in the world' rather than 'out of the world' - since gods were embodiment of natural and man-made phenomena, having them manifest often was a logical consequence, whereas monotheistic religions defined gods as distant and, as such, much less likely to manifest. Furthermore, the more centralised the religion and the more powerful the church is, the more controlling it will get, including on verification of 'miracles'.
So, really, it depends on the religion. I can easily see some religions taking the report of a divine intervention as "OK, you met the god(dess), (s)he gave you a divine mission, fine. The road is that way.". I can also see other religions being much stricter on acknowledgement of such intervention and requiring a full inquiry, with interview of unbiased witnesses and a study by theologians of the church to make sure that the divine intervention is real and is not heresy (diverges from canon), because the last thing a powerful, centralised church wants is a miracle that invalidates part of the dogma.
At worst, the character that was the recipient of a divine intervention might be branded a heretic and hunted by the church so that they don't "pollute the minds of the faithful with their lies".