This is a vast oversimplification, which only sounds plausible if you pretend that energy production scales linearly with demand. In the real world, if there's a plant producing more than its consumers demand, the reason for the excess capacity is to accommodate spikes and future growth. If you come along and build a BTC mining rig next door, that "future growth" has arrived sooner than expected, forcing the utility to build new capacity years ahead of schedule (presuming it's feasible to build it at all), resulting in significant price increases, their refusal to sell you as much electricity as you want to buy, or both.
The (amortized) cost of building out new supply is a major[0] part of the cost of electricity - this is why most big energy producers spend millions of dollars per year on energy efficiency incentives. Haven't you ever wondered why your power company will give you a $50 rebate on an EnergyStar dishwasher? Isn't it counter-intuitive that they would pay you to buy less energy, when they have excess? It's not because they're tree-huggers - it's because decreasing demand growth delays the day when they need to build a new plant to meet demand, which increases the profitability of the current plant enough to make those incentives cost-effective[1].
0: I can't find a good estimate and it varies by fuel type, but I rememeber an environmental engineer at a former job telling me it was about half. Look up "Levelized Cost of Electricity" for more info.
1: If you're not convinced, instead of demanding more details, I urge you to just stop and ask whether the proposition "There is a lot of excess energy production lying around which BTC miners can soak up without impacting everyone else very much" really passes the sniff test.