Read that last line again. It's the fossil fuel industry that is encouraging him to stay in the accord.
There is an interesting quote from an industry insider near the bottom,
"The independents are anti-climate change ... all this stuff costs them money. The global companies operate all over the world. They have to operate at one standard - the highest standard - wherever they operate.”Ah! Now it's starting to make sense. I don't think the international corporations care about the environment any more than the small independents. I'm sure they would gladly throw out all regulations and pollute to the maximum extent possible if they thought it would improve their profits. But, they have to work with international laws, not just US regulations. It is easier, and more profitable, to have one set of regulations instead of multiple ones. The locals don't care about the international laws anymore than they care about the environment. They will pollute as much as they can get away with and chaff at any kind of regulation that might impact their profits.
This presents an interesting dilemma for the fossil fuel industry. They want the US to stay in the Paris Accord but, at the same time, provide funding for the anti-science advocates to prevent any actions being taken. They are, in fact, working both sides of the table.
In the end, regulations will be put into place to limit greenhouse gas emissions. People like Trump and Pruitt and organizations like Heartland Institute will all fall to the wayside. The only question is how long will it take.