If the forests arent thinned dont they just burn down
any way when the underbrush gets heavy?
Not redwood forests. The big trees are essentially fireproof. Due to the soil that develops under them and the constant shading, there usually isn't very much underbrush anyway.
Other forest types you are correct.
In redwood country, you'd be lucky to even get a match lit because of the year-round soggy weather. That's why those forests are ancient.