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Um, no. You don't base your usable gas for a dive on the amount of gas you started your last dive with.
I agree with most of your last post but absolutely not this.
I was thinking the same thing as I read @halocline first post, but I can see where the logic came from, and I agree that the original point of 1/6ths wasn't to give additional gas to "solve problems", but to "limit penetration".
Rule is 1/6th of doubles, or 1/3's of singles. If using al80's filled to working pressure, that is 1000psi "total", being 1000psi out of the one tank, or 500psi out of each tank.
His instructor probably interpreted that as you are allowed 500psi of penetration, and provided that the 500psi does not exceed the third of the full capacity of one tank, then you are fine. i.e. can't do a 500psi penetraion if your tanks are at 1200psi, but you can do it if you start at 1500psi.
Now, will the agencies agree with that? Probably not, but I don't disagree with it, and I think it is much more inline with the spirit of the original rule than what is being interpreted.