Forgive me for asking the obvious. I know it seems self-evident but do we know for a fact that cleaning underbrush would avoid wildfires or is everyone just assuming it to be the case?
No, but it would stop fires from becoming too big and killing the crowns of the trees, which kills the forests. Forests naturally burn every 20 years or so, which burns up the dried up fuel. Also, after only 20 years, the amount of fuel is not enough to produce a crown fire, so the forest will survive the fire.
But now after 100+ years of stopping forest fires, so much fuel has built up, when a fire starts, it will become a crown fire. It also will burn so hot it becomes impossible to stop.
Unfortunately, Alan's idea of cleaning up the forest floor has a few of issues with it. First, there is just way too much land to clean. Second, no one really knows how much fuel needs to be removed. Thomas Swetnam, a scientist in AZ who studies this, cleaned up a forest near him and they thought it was cleaned up enough to not produce a crown fire. A fire came through shortly afterwards and it became a crown fire and killed the forest. So really no one knows how to solve this issue.
More than likely we will have to deal with severe forest fires for many years to come until all of the forests are cleared and begin growing again. The downside to this is it takes about 100 years for a forest to even start to develop, and by that I mean for trees to re-enter the land.