I built flat board doors, without backing support, for a bathroom vanity (plenty of humidity) 10 years ago that are still flat. I believe one of the keys is to carefully select the individual planks and arrange them properly.
First, choose wood where the rings extend through the thickness of the board, rather than its width. Boards will warp more easily across a wider span of an individual ring. The greater the width of individual rings on the exposed face the more it will have a tendency to warp. In addition, since the rings in a tree curve there will often be more rings at one part of the board width than at other locations. Wood will tend to warp more when there are fewer layers of rings and uneven numbers of them. If the grain runs parallel with the board face then there are few rings and different numbers of layers the board is more likely to warp across its width. You can identify these boards by looking at their face which will have a 'cathedral' grain pattern, or examining the end where there will be a few ring lines running closer to parallel to the face. On the other hand, if the board face presents many parallel grain lines, its original face orientation was more likely parallel with the radial axis of the tree. It will have less tendency to warp.
So to make a door panel choose wood where the grain lines run primarily perpendicular to the face. Make certain they are fairly uniform along the length of the board. Changes in grain direction can play havoc with the flatness of the board over time. In addition, limit the width of each board in the panel to 2". This will limit the amount of warp force originating from any one board. Next, alternate the direction of the grain of each boards so that any warping force from one board is cancelled by the next. Look at the end grain. If board grain angles left to right on one board, make certain the adjacent boards direction angles in the opposite direction. Finally, completely finish the door panel, inside and out, to allow for uniform moisture transmission inside and out.