Well, I did a bit of research. Basically the idea is to find a bit of old furniture, or make something a bit rusticated to start with, and if you feel like it, give it a bit of a sand, apply paint, then get some abrasive paper and/or sponge sanding blocks, and sand the paint off a bit at corners, edges, arm rests, stretchers and other places that would be liable to normal wear and tear. It probably fits quite neatly into the 'upcycling' trend that seems to be a thing nowadays, and is kind of aligned to a style of furniture I've always known simply as shabby chic. Here's a link to an example of the technique: Slainte.
It is annoying that the photo has gone, but it wasn't as you describe here. It looked more like the piece had been finished with a bandsaw and varnished, but it was smoother than if it had been prepared that way. It wouldn't have looked out of place as a fake rustic chain pub table. It looked fake rough rather than fake worn.