Mostly true
First, your title somewhat overstates Reason's claim in the article "Bad Policies Fuel Fires", which is that "[politicians] and environmentalists increased the risk of big fires by opposing the thinning of forests." The article never claims overgrowth is the sole reason (or even the principal reason), just that it provides fuel to make wildfires larger and more devestating.
Second, understand that "enviromentalists" is a broad classification, not a single unified group. As you look at actions of certain groups, realize they don't necessarily characterize every "environmentalist."
Third, overgrowth indeed causes larger wildfires, a fact agreed to by all sides. In 1999,
Years of aggressive firefighting have allowed brush to flourish that would have been cleared away by wildfires, said Michael Paparian, a Sierra Club senior representative in Sacramento, Calif.
While the timber industry and environmentalists agree the forests need thinning, the timber companies want it to include more logging than the environmental groups want.
“There’s no magic solution to the condition of the forests. Our forests have gotten into their current state during 150 years of human manipulation,” said U.S. Forest Service spokesman Matt Mathes.
https://www.latimes.com/archives/la-xpm-1999-aug-29-mn-4883-story.html
Fourth and most significantly, in multiple high-profile instances, environmental groups have successfully opposed proposed solutions to this problem.
In 2002, Senator Feinstein (D-CA) blamed the Sierra Club for blocking a bill to thin forests with logging.
Sen. Dianne Feinstein blames environmental ally the Sierra Club for Congress' failure to pass legislation last month to thin national forests to reduce wildfire threats in the West.
"You have a very polarized community when it comes to fire and how they view fire," Feinstein said.
"The Sierra Club roasted me," she said.
https://archive.vn/fQ5RZ
In 2009, an LA County supervisor blamed environmentalists for being unable to do controlled burns.
Some critics suggested that protests from environmentalists contributed to the disaster, which came after the brush was allowed to build up for as much as 40 years.
"This brush was ready to explode," said Los Angeles County Supervisor Mike Antonovich, whose district overlaps the forest. "The environmentalists have gone to the extreme to prevent controlled burns, and as a result we have this catastrophe today."
http://www.nbcnews.com/id/32664068/ns/us_news-life/t/efforts-clear-brush-la-fire-fell-short/
In 2014, the Sierra Club opposed a failed Republican bill to make it easier to thin forests, something that would help the overwhelmed Forest Service.
As written, the bill would amend an existing law designed to help clear out forests clogged with flammable underbrush called The Healthy Forests Restoration Act.
Heller’s proposal would further loosen environmental procedures for hazardous fuel projects, allowing them to avoid review altogether if they meet certain criteria...
But there’s a catch, says Ani Kame'enui, a forest representative for the Sierra Club...the bill is undermining a bedrock environmental law to achieve its aims of ramping up commercial logging on public lands.
There is no doubt the Forest Service is strapped for cash. After last year’s sequester cuts went into effect, the wildfire fighting budget was slashed by $115 million.
Instead of undercutting environmental laws, Kame’enui says the answer is to address the funding issue through efforts like the Wildfire Disaster Funding Act...so that federal emergency dollars could kick in to help cover the costs.
https://www.hcn.org/blogs/goat/can-loosening-environmental-laws-tame-the-wests-flammable-forests
Summary
In multiple instances, environmental groups have successfully opposed proposal to clear forest growth. Strictly speaking, the claim is true.
However, it fails to provide the reason for opposition. Those environmentalists fought those the forest-thinning not because they disagreed with the diagnosis, but because they thought proposed approaches cut corners.