When doing some digging about the nature of Bajoran orbs I found an interesting piece of unused dialogue spoken by Bashir in the episode 'Accession' when discussing the neurotransmitter psilosynine:
"It's a neurotransmitter involved in psychic phenomenon [sic]. We all have a little of it, but people who've been exposed to things like... Vulcan mind melds... the Bajoran orbs, are often left with more."
This draws on canon information from TNG stating that psilosynine is chemical used in Betazoid telepathy- which is among the more powerful versions we have been shown. Since the Orb's increase the amount of this chemical in the brain it may convey telepathic ability.
We know that telepathic ability can be granted in this way from T'pol and Tucker's experiences. After melding they experienced a profound psychic link far beyond what a human should be able to experience. But as Bashir notes both mind melds and the orbs increase psilosynine.
Another interesting tid bit is the Bajoran clergy's annoying habit of grabbing ears to read one's 'Pagh'. However some, like Opaka, were able to gain uncanny insight into those they touched. While this might all be a strong example of good research and cold reading Bajoran spirituality touches on enough metaphysical (in a very literal sense) areas that we can keep an open mind.
Given that the clergy keep the closest presence to the orbs and consult them often it is likely they have a far higher psiloslynine count than most. If Bajorans have a psychic potential then then the clerics are the most likely to express it.
Further evidence for this is the Sidau village from 'The Storyteller' Bajorans born and raised in the presence of even an Orb fragment develop powerful psychic abilities together including telekinesis and energy manipulation.
Its possible then that Bajorans are touch telephaths- when their brains are sufficiently stimulated- such as by the orbs. This explains how they are able to form such insights not to mention their prediliction for prophecy. Whatever connection the Prophets, the wormhole and the Bajorans have it is clearly a deep one- influence their culture for tens of thousands of years. Is this enough time for psychic potential to evolve? Hard to say but given that spatial phenomena can unlock telepathic potential in humans- such as with Gary Mitchell and Elizabeth Dehner its not outside the scope of possibility that the same could happen to Bajorans.
If the unlocking of Bajoran potential continues then this may form the basis of the link between the Bajorans and the Prophets. If the Bajorans continue to evolve into psychically powerful beings beyond space and time then they may indeed become their own gods.
And why they were so out of sorts weeks later during 'The Cage'