That isn't completely true. A well managed forest will sequester some carbon when it burns. Note well managed in there, that means a small fire every year, a large fire gets hot enough to burn all the carbon, but a small fire will burn only part of the carbon and leave the rest as charcoal. Moral: shoot smokey the bear and let foresters start the fires they want to if only they were allowed to.

Of course the above is a generalization, and as all of them false in some way. Ask your local forester what applies to the forest in your area, but don't try to apply it to a forest in the next neighborhood as that might be different.