Just so everyone really understands this, the cost of running a typical fan for 24 hours is about seven cents (24 watts @$0.12 k/w). Turning the fan off for an hour saves $0.0029 cents.
I point this out, not to deflate the OP’s claim that the fans are wasting energy, but to help folks illustrate how inexpensive electricity is, compared to the life-saving effects of air-conditioning during a heatwave. There was a story on the news last week about an elderly woman who had died, and whose son said the mom kept turning the AC off when he left because “it cost too much.”
A small window unit that draws 500 watts costs six cents an hour to run, or $1.44 to run it all day long. It’s probably wasteful to run it when it’s 60 degrees outside, but the idea that you’re saving money while you’re sweltering is poppycock.
As for the OP’s question, she is right. The fans work by creating a wind chill effect, not by actually cooling the room. No benefit is created when the room is empty. However, that’s not the case if we’re talking about an exhaust fan which is pulling hot air out of an attic, for example. it’s also not true if the fans are used in conjunction with A/C units, and thus assisting in spreading cooled air to other rooms.