Then we must agree to disagree.@Brian D For simple circuits such as a diode and resistor it generally rings true. A simple example of where this does not apply is a device that uses a transformer. Assuming for this example the transformer has 100% efficiency watts in equals watts out. Utilizing a transformer you can alter the relationship between current and voltage. Most devices using a transformer have a 120/240v switch. The primary is center tapped to accommodate a secondary voltage input.
With more complex circuits and some other components this relationship isn't always linear. I recently converted an audio DSP for use in 12v. During testing I analyzed current draw at various voltages. At 12v the device drew 200mah. At 6-9v it drew slightly more. When I dropped down to 4.5v the draw was slightly less than 200.
Current–voltage characteristic - Wikipedia
I used the example for both AC and DC where the load does not change. If one increases the V to increase the I then R must change. That is a law that cannot be broken.
But we are getting OT.