I have personally experienced and done no touch throws.

No magic.

IMHO, its about timing.

One way is easy with attackers who over commit and extend. Technically they are depending on you being there to get hit and support their attack. If at the last second you move off the attack line, there is no support and the person falls by their own momentum.

I see what you are saying here but you are not throwing them, they are falling because they have over extended and lost balance.
The other timing is by not moving too fast or too slow. If I irimi too fast, I hit the guy. Too slow, and they intercept it. A middle speed allows the mind to detect it and attempt to evade it. The evasion takes the balance.

Just my take from my own experience.