But we do physically step out of the rift at Adamant, going from the Fade and back into the mortal realm. We were there, and then we weren't. Similarly, we see ourselves run through the rift in the Fade memory sequence with the Divine, and also see our followers run through before Nightmare blocks the path. Cassandra (I believe) also describes it in such a way at the start of the game when she relates the events of finding the PC.
This is different from, say, the Fade experience in DAO where we clearly fall unconscious and then stand back up when it's over. The same happened again with the Fade in DAA; when it's over, we are shown to have been unconscious and then rise again afterward.
And what does the Inquisitor say, exactly?
Well I was just refreshing my memory by reading the wiki on the fade, and the lore of all the cultures presented so far, even the Qunari, seem pretty consistent that the fade is some sort of metaphysical realm.
What I mean is, they could have simply been perceiving the fade while fully conscious, with their physical senses as well, as opposed to just with their metaphysical or psychic senses while asleep or in trance, the way fade travel is normally done.
This is supposed to be really difficult and dangerous, and was said to be done by opening rifts. But the ancient Evanuris apparently knew of this practice, and since they had a conscious connection to the fade, they might have been fairly skilled at it. The Crossroads was an example of a quasi fade/physical realm.
Maybe it would help to compare to real world metaphysics/philosophy. I'll try to explain where I think they might be going with it. I'm not saying they are definitely basing the fade on this general idea, but it seems likely.
Anyway. The way that experiencing the astral realm is said to work, is that you have more than one "body" - a physical body (including your 5 physical senses, sight, touch, smell, etc), and an astral and light body (which are spiritual and mental, and that you perceive or "see" with the energentic senses associated with those bodies in the associated metaphysical plane). The three "bodies" are attached and interconnected to one another.
Astral travel/projection then, is said to be the practice of separating the astral body from the physical body. The physical and astral body are said to be connected by a kind of thread or umbilical cord like structure, the so called "silver cord". As long as that cord is still attached your body remains alive and you can return to it. But once the cord is cut, you have fully crossed and can no longer go back. This is what some speculate happens when death occurs, and is what people have described seeing in near death out of body experiences. So you can see from this how something like Tranquility might work by "killing" someone in the fade. They are severing or binding the astral body, perhaps. And entering the fade physically could be perceiving the fade with the physical senses consciously.
Or not. I'm pretty sure I'm way over thinking it.

Oh yeah, the Inquisitor told Iron Bull that the Veil is not a physical barrier but more like a vibration or frequency that is holding the fade back.