No, actually, "greenies" figured out a long time ago that you need controlled burns and other active methods to keep forests healthy. Total suppression of fires dates back to the 1940s, when "greenies" weren't really around, and forest management was not well understood by anyone. After a few decades of total suppression, scientists realized in the 1960s that fire was an essential part of forest health.
The problem now is less about knowledge, and more about actually spending the money to protect forests.
"Greenies" also usually object to building communities in areas that are prone to fire. E.g. they are currently opposed to a "Centennial," a massive development near Los Angeles on a former ranch that, among other issues, is vulnerable to wildfires.
We should also note that something like clear-cutting forests (which environmentalists generally oppose, and people like Zinke suggest) does not actually save forests. That's like saying "you can cure lung cancer by killing the patient."
Annnnnd.... About half of the forests in California are under federal management. Since you missed it, we've had quite a few Republican administrations over the past ~50 years. Even with Democratic administrations, environmentalists don't often get their way.
Finally, unlike the Zinkes of the world, "greenies" realize that global warming is now a major threat to forests. Higher temperatures result in drier forests, which means that fires are more likely to spread faster, and be more intense. Just to be clear, AGW is not an example of "nature taking its course."
