You're not too far off the truth, but it's only a half truth. The global warming/climate change cultists are getting their money from big-govenment sources that have at least as vested an interest in producing results that can be used to argue for increasing government authorities and funding as the oil companies have in the dissenting research. This is a common fact of life in academic research - funding sources are never perfect.
Ethical researchers will not compromise their results, and take what funding they can get as a result. They may go from one source to another frequently in order to keep working, and typically run on a shoe-string.
Unethical researchers find a good titty and make sure their results always line up with that prominences interests without needing to be told. Whatever their other problems, they tend to do very well at keeping the funds flowing and that counts for more than any of us really want to admit.
The people that are best at funding in climate research decided years ago that anyone who denied their faith in 'global warming' were not to be reasoned with but rather to be excommunicated, shunned. They have turned their departments into churches, and away from science. You cant even get a passing grade, let alone a degree, without mouthing the creed obediently. If you manage to get a degree before you start doubting them, you still wont get funding from anyone except the fossil energy companies, so it wouldnt be any surprise at all that they are funding virtually all of the real science that's going on in the field today.
And sad as it is (they are figuratively fossils themselves, and need to die) it's still better this way than if they were not doing this and NO ONE would fund climate science anymore, period.