No, they’re arguing that the price of power should be split:

• A fee for grid maintenance (equal for all)
• A fee per unit of consumed power (scales linearly with consumption)

This makes sense, because regardless of you much power someone uses, the costs associated with maintaining the infrastructure that allows them to draw any power at all remain the same. This also happens to be the model used in Norway, so it’s not an untested concept.

Another option, relevant when the cost of building the power plant is large and the cost of energy production is negligible, is that everyone connected to the grid pays a near-flat fee in total, which is distributed among consumers depending on how much power they use. I’ve never heard of that option being used before.