Mixers are non-linear devices. If you reduce the power level of the strongest component going into a mixer, the power level out of the mixer will drop by more than the original reduction. That's close enough to draw the conclusion that things downstream of the attenuator are operating in a linear manner. This is confirmed by the fact that greatly reducing the level of the local broadcaster with the ICE filter had no measurable effect on the level of the mixing product. The conclusion is that the mixing is occurring before the receiver and is being re-radiated and received on the antenna.
Mixers are essentially diodes.
Some mixers use more than one diode for greater efficiency, but in essence all mixers use diodes to provide the necessary non-linear element. Any metal object touching another metal object can set up a diode through point contact rectification. It was an early example of a diode made by point contact rectification. I once worked in the field of space and satellite communications. Antennas designed for this service are usually used for simultaneous transmitting and receiving.