Of course they overplayed their hand, it was the only way to get funding. One side of this debate got funded and the other didn't.
For years the oil companies were heavily funding people to create doubt about climate science. They eventually got publicly outed for paying for bad science, and stopped because it looked bad.
As for atmospheric science, the main funding for atmospheric science is in improving weather models, including hurricane path predictions and aviation weather. Climate predictions are pretty much just another application of the models made for other purposes.
As for the oil companies, they shifted their strategy to funding "think tanks" pushing libertarian ideas, funding advocacy that the government needs to avoid taking any action on climate change.