Certainly true that you can only use stock as wide as you can flatten, but my point about the boards holds true. The point is you need to learn to make panels that won't cup or warp. If the wood isn't well seasoned, don't use it until it is. After that, there's no excuse for cupping or warping if you handle the material correctly. Not to mention the fact that as I mentioned, the panel is trapped in a groove, it should not be able to warp or cup as it's held on both sides. The pressure of wood warping is not like the near unstoppable force of wood expansion. Too often woodworkers are given these pieces of advice as gospel and will build by them for the rest of their lives. You should compose the panel to be as aesthetically pleasing as possible, and then treat those boards in such a way that they will not give you any issues. There's virtually no reason to use skinnier boards or alternate end grain etc. Skinny boards are easier to flatten and square, and I suspect that's the origin of the advice. And the expansion rate of the two faces of a board, even flatsawn, are so close that alternating grain patterns makes no sense except possibly on very soft woods...possibly.
Most if not all cupping or warping that occurs after the wood is properly dried is caused by woodworker error. Not letting boards acclimate, taking more material from one side of a board that's not an even MC% all the way through, uneven finishing etc. The obvious exceptions being exterior doors and the like, or extremely thick planks 12/4+. But between 4/4 stock 3"-12" wide? No. Warpage like that is due to uneven releasing of stress or uneven moisture and is easily avoided.