Perhaps because English isn’t their first language, the terms used can confuse.
To me, what they were saying was that the laws of thermodynamics demand that heat flow (unaided) from hot to cold; never from cold to hot.
Sure, the atmosphere acts as a blanket, slowing heat transfer from Earth to Space, but no, the blanket isn’t radiating heat back to the Earth itself (their point, as such would violate the laws of thermodynamics).
So since we know that the atmosphere isn’t getting thicker...and since CO2 is such a rare trace gas in the upper atmosphere...
...then we know that either CO2 must have super-amazing insulating ability...or that the so-called “Greenhouse Effect” is in error.
Need to mention the JoNova website and Dr. David Evans...
He has a paper that addresses the issue as to whether the predictions of an atmospheric hot spot due to CO2 occur in real world measurements...They seem to be hidden or nonexistant.