Let's be absolutely clear that this is only true for a limited number of forests. The evidence for this is the existence of very old trees.
Unfortunately many forests will become increasingly susceptible to fire as dry seasons are extending in many areas due to climate change.
Lots of tree species are able to survive a forest fire once they reach a certain size. There absolutely are very old trees in areas that burn frequently.
There also always is plenty of oxygen. In dry summers, there’s also plenty of fuel. What’s lacking is sufficient heat. The ignition temperature of wood is difficult to assess, but wood can start burning at 125°C ≈ 256°F (https://www.warrenforensics.com/wp-content/uploads/2016/06/P...)
It doesn’t get that hot without help, e.g. from a campfire, a magnifying glass, or sparks from electricity.