They talk like that because it's actually true in one sense. There are a lot of side-effects of capitalism that aren't accounted for in a business' costs. It's the tragedy of the commons. We all share a common environment, but there's often no cost for harm to that environment.
On top of all that, developing nations are trying to get to our living standard. To do that, they'll be harming the environment as well in increasing amounts, so it's necessary for one to consider that as a factor.
A common way to consider these issues is to issue carbon credits that one can spend. If your business doesn't need them, you can sell them to another business which creates a market for them (and hence a cost). If you do something that reduces emissions you can get more credits. Every country would get some and could trade the credits as well. To help developing nations, they would get a larger share of the credits which would naturally limit the increase of CO2 emissions that the developed nations would get. But, if the developing nations don't need the credits they could sell them to the developed nations to get things they need.
That's all a pretty simplistic way of putting things and the system is far more complicated, but that's the overall idea.
So, it is a redistribution of the world's wealth, but it's still a capitalist system.
The problem is that if you don't give the developing nations something, they won't sign on to the agreement and they could build a lot of cheap but polluting plants and equipment and make things that much harder on the countries that do sign the agreement. It's all very tricky.
A friend of mine did his PhD work on energy planning in developing nations and he focused on India (and went to live there for a year, I was his remote tech support). He's now a senior person at a NGO that does work in developing nations so I've heard him talk about this at length before.