Just guessing. Is it possible that non-magnetic stainless steel doesn't have enough of an iron content to make the induction work?
Austentic stainless steel has about the same amount of iron in it that magentic stainless steel contains. In fact, if heated to around 700 degrees F., or cold worked, such as by rolling or extruding, it will become magnetic.
And as for the workhorse of the stove being like the winding on the armature of the motor, that isn't exactly correct either. The winding in the stove is analogous to the primary winding in a transformer, with the pan acting like the secondary winding, where the current is to be induced. The part about the alternating current is correct. I creates the expanding and collapsing magnetic field that cuts the pan metal, thereby inducing eddy currents that create heat because of the pour electrical conductivity of the ferrous metal.
Please see the following URL for more info about austentic steels and their properties -
Stainless Steel - Magnetic Properties.
My point is probably moot though, as I don't know of any cooking vessels maid of austentic SS.
And magnets will stick to enameled CI pans just fine. I have seen advertisements that state that these pans will work with induction stoves.
Unless there is a safety sensor that senses the magnetic properties of the pan sitting on the burner, I don't know why non-magnetic stainless wouldn't work on an induction stove. Aluminum and copper won't create enough heat, as they are great electrical conductors. That's why they are used in all kinds of wiring, including high power transmission lines. And the induction of current is evident in dynamos, generators, magnetos, and alternators, where a copper wound rotor is spun through the fields of permanent magnets to generate electrical current that powers our homes, industries, and cars.
Simply stated, it is the ability to have a current induced through the conductor, and the natural resistivity to that current, exhibited by iron and steel that make cooking with induction stoves possible.
Seeeeeya; Chief Longwind of the north