You're right. It really does make no difference other than time it takes for IR to leave earth. We're talking femtoseconds. Alarmists butcher it even more by suggesting energy x1 can be reused as it bounces back and forth from GHGS to surface accumulating energy each time when it's the same energy to start with.
On another point if the theory was true you would be able to make a space craft nearly perfectly insulated from losing heat via radiation with just a reflective mylar blanket with the right wavelengths of reflection even if it was receiving no energy from an outside source but clearly that would be a violation of the second law. After the first absorption and re emission there's several orders of magnitude of energy reduction and it would be at a lower energy state than whatever the emitter was so there wouldn't really be a way for it to raise the temperature of the system.
Yep they are disregarding thermodynamics. Take a coke bottle filled with mostly water and co2 the amount of co2 and hence pressure in the empty non liquid space is governed by the temperature of the solution nothing else. Co2 increases we are seeing are resulting from heating caused by the sun this should be apparent immediately once you understand the level of co2 in the atmosphere has been both lower and higher than current day even in the geologically recent past.
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