Fake? Accurate? Neither?
There is reason to believe that at least one of the emails recently leaked from the Heartland Institute was written by someone who sounded entirely too much like a caricature of “climate denialist.” It's possible that that they really were written by such a caricature. A large fraction of college students graduate believing with a perfect faith that fossil fuels are likely to melt an icecap or two and that becoming a climate-denialist flack is a job suitable for conscienceless scoundrels. Some of the people believing in that claim are such conscienceless scoundrels who then try to get jobs as climate-denialist flacks and a few might even succeed.
I'm sure that the think tanks have screening procedures to keep people like that out but they might not always succeed.
If you want examples of similar phenomena, you may recall that the campaign against drug re-importation was run by people who thought it was their job to defend an oligopoly. For another example, there was a lunatic on parts of Usenet who actually believed left-wing conspiracy theories about the triumph of Turbo-Capitalism but decided he wanted to ruthlessly claw his way to the middle. People like that actually exist and might be at work here.