It is you who makes the false claim. In my website http://whyitsnotco2.com I have offered AU $50,000 to the first who can prove wrong my hypothesis that is based on correct physics and who can produce a counter study to mine that showed that the greenhouse gas water vapor cools the surface.
Please consider reading my three reviewed and accepted papers written in 2012, 2013 and 2016 and containing breakthough science not yet found anywhere else in world literature, but supported by copious evidence, as all correct science should be.
The “Radiative Forcing Greenhouse” hypothesis is based on nothing but fictitious, fiddled physics wherein the laws of physics are applied in inapplicable circumstances and, in some cases, just ignored.
Greenhouse gas can only cool, and it is just as well that water vapor does indeed make rain forests slightly cooler than deserts at similar latitude and altitude, as shown in my study in the Appendix of my book “Why It’s Not Carbon Dioxide After All” and my paper “Planetary Core and Surface Temperatures” which nobody has proven wrong since it appeared early in 2013. All three papers (and three videos) are linked from the above website.