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OK, Now I Have a Question I Need Help With

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I ran across a forum discussion that got me to thinking <link>.  I was researching (again) measuring power with some non intrusive method when I ran into a typical snarky set of responses to a person showing a possible solution.  The author of the post showed this picture of a clamp current meter and some wiring:
Granted, it looks like it won't measure anything since both lines go through the current clamp, but I'm here to tell you this works.

Yep, if the direction is reversed using a loop in the wire it will measure total current through the two lines.  I actually tried it with a current clamp and some 14 gauge wires to a 220V light bulb in an Edison socket.  As further proof, here's a picture of the wiring inside my smart meter:
Look closely, you can zoom if you need to, but notice how one of the power legs goes through the current transformer in the opposite direction?  Here's another picture of the wires removed from the meter:
One current transformer and two wires to measure the total current being used by my house.  I asked the guy from the power company why they didn't just put the current transformer around the neutral and he said people could avoid part of the bill by referencing to ground avoiding the neutral path.  That actually makes sense in a very unsafe fashion.  There's a number of things you can do with current transformers that I hadn't thought of until now.  You can run both wires through in the same direction and tell if there is current to ground; that's how the GFCI you have in the bathroom works.  You can loop a wire around the transformer and double the voltage out to measure smaller currents.  Heck, there's a bunch of configurations that can help us measure things if we learn how they work.

My question is, how the heck does this work?  I know it does, I've done it, and the meter manufacturer has also.  I just can't get my head around the physics of it.

This also points out how folk on the web jump on someone who is correct and belittle them.  I guess we've all been there some time or other.  The author of the picture showed a heck of a lot more restraint than I would have in the same circumstances.

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