This is getting silly. The current on the inner surface of the pipe is an eddy-current, there is electrical resistance and loss of energy, and it changes the impedance of the loop.
The eddy current doesn't reach the outside surface of the pipe until and unless it magnetizes (it's too thick to do so at the frequency of interest)
The "net result' is an impedance change in the loop, and yes, the B-field outside the tube is the same as if the tube hadn't been there, UNLESS the impedance change loads the generator. Eddy currents don't cancel the B-field caused by the wire. There wasn't any hope that they would: the geometry is wrong. The only way to make current in the pipe to cancel the B-field around the wire, is to make a net axial current. There aren't any electrical connections at the pipe ends, so there's no net axial current; Kirchoff insists.