This is incorrect. The magnetic flux will induce an electromotive force that will cause a current to flow in any conducting material and cause heating if this material is not superconducting.
As an example, induction heating is a commonly used method in zone melting for Si-purification [0].
The effect is more pronounced in ferromagnetic materials because a larger flux is induced.
A myth. Copper and aluminium won't heat on a consumer-grade kitchen induction stove, which only have a set of coils designed for ferrous metals, but restaurant kitchen professional IH stoves can use the different frequencies that heat non-ferrous metals, and a forge or melting furnace can indeed melt any metal, ferrous or not.
Why don't residential induction stoves have that capacity? Given the popularity of aluminum and copper cookware I'd think it would be pushed out. It's one thing people always bring up with induction ranges.
The electronics to drive the right frequency for efficiently heating ferrous metals (about 25KHz) are affordable. The electronics to drive the much higher (at least double?) frequencies for non-ferrous metals safely are not so affordable. It would add more to the cost than a new set of cookware. Cast iron is the king of cookware and works great on IH, anyway!
You can put a few mm thick piece of steel on top of the hob and then set your copper pan on that, as a workaround.
