I know this isn't "standard", but the way our GM is playing it, there really isn't any Veil. Most of the seriously mythical stuff happens in what I have come to call terra incognita.
The quest to get Aengus' magic harp back took us into:
- The land of the fire giants, accessed from earth by going off the coast of Ireland to a lava vent on the bottom of the ocean, and down a lava filled lava tube
- Going into the land of Crom Cruagh, accessed from the land of the fire giants by going into a giant Sarlac mouth and falling half a kilometer into a swamp
- Escaping Crom Cruagh through a tower that leads our of a Sarlac mouth into the middle of an unknown ocean, where we had to swim for days
- Ending up on the shores of the land of the Tuatha de Danaan, from which there was a secret shortcut through the land of the Fey to get back to Earth.
There are numerous catches and gotchas. The land of the fire giants has no water, the land of the fey bewitches anyone who eats the food, in Crom Cruagh everything is diseased and poisonous, and everywhere there are things that want to eat YOU.
Basically, any human that wanders into such a terra incognita would have to wander pretty bloody hard to get there in the first place. At which point they'll probably get eaten, enslaved, ensorceled, go Jumanji, or just die.
Back on Earth, our GM isn't making any effort to keep a Veil up. Members of my band have been detained by a secret government agency similar to the bureau in X-files, or a very watered down Laundry from Stross' Laundry novels, or a (so far) toothless BPRD from Hellboy.
This happened, because there is video surveillance everywhere, and they're not making any effort to hide their powers, and being detained was completely ineffective because they simply walked out of the underground bunker, taking chunks of wall with them like the Juggernaut.
The reason the existence of titans and scions and gods isn't common knowledge is because they keep mostly offworld, and because very little action happens on earth, and because the scions have really great spin doctors. Like Loki.
Fatebinding has not been limited to the humans we interact with while on Earth. While one or two members of the band picked up fatebindings to humans, some of us have gotten fatebindings to titanspawn. I'm angling for a leprechaun or succubus.
To conclude, "non-awakened" humans can wander into terra incognita, but it's pretty hard. It's really easy for them to get involved in any adventure or doings that happen while on Earth, and it's really easy for a band to involve someone in their actions. At which point the rules for fate-binding decides whether they get dragged in or not.