Science is what is published in peer reviewed journals and presented at conferences. What is not science is to make allegations of errors and not follow up on that with peer reviewed publications, conference presentations etc.
Now, I'm not an expert in climate scince, so I can't give a detailed response to problems raised by skeptics. But it is up to the skeptics to make their point in the scientific community. So far they haven't so their criticism of global warming theory is definitely not science.
I think this statement is complete rubbish. Any proponent of any scientific proposal (including AGW) must be completely open to challenge and analysis from any quarter. That is the only way to ensure credibility. If someone postulates something, it isn't up to the rest of us to prove the opposite and get published in a journal as part this. A very good example is the recent case of the 0.15 degree error that was found in the ground based US temperature reading post 2000. These were simply pointed out by a Steve McKintyre .... and I may be mistaken .... but I don't think his observations were peer reviewed or published in any journal. And that was science at its very best.
The adjustment to the temperature record was not significant,
see here. Anyway, in science everything is peer reviewed. Of course, one can always contact a scientist and discuss some issue. That can then eventually lead to a peer reviewed work.
AGW has already been proven to the satisfaction of the climate scientitist. There have been many thousands of peer reviewed articles on this subject. So, it is established science. It is effectively challenged all the time when scientists do new investigations. These investigations always lead to scientific articles that confirm AGW. So, it isn't a mere postulate anymore.
In case of some untested postulate you could indeed say that the proponents of that postulate should invest some time to respond no non peer reviewed criticisms. However, in case of AGW, we have long passed that stadium. It is really similar to Evolution vs. Creationism, where the scientists do not respond to every criticism raised by creationists against evolution.
