Mostly true.

Women had to wear something during their menstrual flow to keep a cloth pad against their body.

Also, women who rode commonly wore a simple version of men's breeches under their skirts for common decency and comfort. One takes spills, one's skirt gets snagged or tossed up, and in any case it's very uncomfortable to have the leather-covered horn rubbing against the bend of the knee, or the rest of the saddle against the inside of the left thigh. That's at least the Renaissance.

The 1800s pantalet was only a leg cover with an open crotch. Modern panties with elastic leg openings are 20th C. Early 20th C saw what we call "tap pants" as the original panties.

Notice how this coincides with skirts getting narrow and short. When your hem is around your ankles, you don't fear flashing when you bend over. You do when it goes above the calves.

So "no panties" applies from antiquity to the 1900s, but they weren't common before then. The zona was mainly worn for athletic endeavors with a bandeau and nothing else.

The reason women didn't like underpants is that they were wearing voluminous long skirts and still had to handle bodily eliminations. In a khiton with a 4yd hem, not a big deal. But when you start hitting medieval gowns with three layers of skirts to hoist, the smallest of which is 3yd and the largest 6yd, that's a double armload to keep out of contact with the garderobe seat. To have to handle all that yardage, and get panties up and down, too? Catching drips is what a chemise is for.

Then you get into periods with very full gowns. Then you get into the Renaissance where you have to handle the different farthingales (hoops), as well. Wheel farthingales are murder in a WC. On top of that, the steel corsets didn't allow bending. Bumrolls went with 10yd skirts. And so on down fashion history until technology like automobiles does away with huge gowns and architectural underpinnings. Then you need (and can make practical) underpants.