As far as I can understand, the stiffness of the boot barely plays a role in causing shin bang. Shin bang is primarily caused when you repeatedly place all your weight on the back of your boots. This can result from poor skiing technique, landing backseat, or both. Regardless of how stiff a boot is, no boot will flex backward, so when you lean backseat, your weight hits something solid, causing strain on tendons and ligaments on the front of your shin. (Imagine jumping on a skateboard deck that is on a rail- the board is going to flex and cause tension.)This results in pain when you try to lean forward again and power the ski. Because the pain is concentrated on the front of your shin, a lot of people assume it has something to do with the flex of their boot, when really the problem originates from what's happening behind the calf. In a stiff boot you might just notice it more, because you will be pushing the damaged tendons/ligaments against something fairly solid.
The best way to avoid shin bang is to make sure your foot can't move in the boot, especially in the upper cuff. If you have a lose fit, then it is easier for your leg to strain flex in a way that results in shin bang, and it will also be easier to slip into the backseat. A tight fitting boot will keep everything where it is supposed to be, helping to prevent shin bang. Of course, it doesn't matter if you have the best fitting boots in the world, if you constantly ski backseat or land big jumps backseat, you will probably still get shin bang, so improvements to technique will go a long way in preventing shin bang as well.
