'You should maybe write a book. ;)'
Why? His 'detection' is not in any way, more clever than simple observation from solving the first 3 layers and seeing that there is either one or 3 flipped edges in the last layer.
'I think you may have solved the 4x4x4 parity problem.'
No, not really. He only made things more complicated than the 3X3X3 reduction method to see that there is parity for a given reduced 4X4X4.
'So I scrambled it up again and re-did it and it worked out just fine.'
Why shouldn't it? After solving the centers, pairing all edges, and solving like a 3X3X3, you should see if the cube has parity or not, right? There is no difference looking at it the way he is telling you.
Honestly, what might interest you is how to solve the 4X4X4 cube using the Cage Method and/or K4 Methods. With the K4 Method, PLL parity is not really a parity, and, in the Cage Method, OLL parity cannot be avoided, however, OLL parity algorithms can be avoided entirely to solve the cube (even if there is OLL parity in the cube).
Parity can be detected even if no edges have been paired at all. The process of doing this, however, is not fun and takes a while to compute (although you will get faster at it if you practice enough: some can do it in 30 seconds). A concept from mathematics is involved, but a relatively simple one. As a matter of fact, this process can be applied to every orbit of higher order cubes up to NXNXN (there is no reason it shouldn't be either: every orbit is treated the same way).