Sorry about the deletion. I thought I'd got in quick enough. Clearly not!

I thought you were saying that the GS theorem becomes false if you weaken the hypothesis to allow other kinds of violations.

I was saying that as far as I knew, the quotation misrepresented the scope of the GS theorem, which did not make claims about other types of violations. You are right that my offsetting externalities counter-example did not rely on this though.

The counter-example I had always been given as evidence that a non-perfectly competitive economy could theoretically achieve Pareto efficiency was that of a perfectly informed, benevolent central planner. However, I readily confess that this does seem something of a cheat. In any event, whether it's technically correct or not, the point is practically irrelevant, and probably not worth wasting any more time on.

I apologise for the diversion.