Is there a symmetry breaker between these two types of experiences?
Yes, repeatability by others.
If we take a basic perceptual experience, we have it reinforced through our lifetimes that our perceptual experience is working by confirming, over and over and over again, that other people see the same stuff we see. And importantly, people who are hallucinating can confirm, over and over again, that other people don't see the stuff that they see.
If you see a cup on the table, you can ask me if I see the cup. I say yes. You can ask a Hindu if he sees the cup. He says yes. You can ask a Muslim if he sees the cup. He says yes. And so on. People who aren't visually hallucinating can confirm with people of all religions (and no religions) that their visual experience is, at least, shared with the people around them.
But if you have an inner experience telling you, say, "My particular branch of Chrsitianity is true", you can ask all those other religious people if they're experiecing the same thing, and they all say no.
Some people get convinced in their lifetime that these experiences ARE as reliable as sensory experiences, because they surround themselves with people who believe the same. A lot of people lose their faith over time when they become exposed to the world of people who don't have the same experience.
If you see stuff other people aren't seeing, you might be hallucinating. Perhaps the same is true for these experiences.