Is it actually cheaper to run a fan AND the AC at the same time, or is that just a myth?

I’ve heard the common advice that "fans cool people, not rooms," which makes sense on a scientific level, but I’m struggling with the actual "frugal math" of it. With electricity rates spiking this year, I want to know if the energy a fan consumes (even if it's relatively low wattage) truly offsets the cost of running the AC compressor less frequently.

If I bump my thermostat up from, say, 72°F to 76°F and supplement with a floor fan or ceiling fan, am I actually seeing a significant net gain in savings? Or is the difference so marginal that it’s basically a wash once you factor in the fan's constant power draw?