Sorry, there is no cheating PV=nRT. n and R are constants. If pressure rises, temperature HAS to rise. This is very basic physics and there is no cheating it. I am an engineer, not a scientist, so I will be happy to have a physicist correct me if I am wrong. In that absence, I am hanging my hat on PV=nRT.
You are absolutely correct that the lowest level of the atmosphere experiences the highest pressure. You can climb mount Everest and see that the air is very low pressure there compared to air at sea level.
But that is not the question is it? The question is, what is causing the CHANGES to planetary temperature. And according to this study, the change comes from increased solar activity causing the atmosphere to increase in pressure. The air at sea level will still be the most dense, but now it is at a higher pressure than when the solar radiation hit.
You can’t cheat PV=nRT.
I'm not arguing that PV=nRT isn't a valid law. My point is that the gas law is NOT the driver of the theory in the OP.
-- And according to this study, the change comes from increased solar activity causing the atmosphere to increase in pressure. --
That's what I disagree with. The mass of the earth's atmosphere hasn't changed, and the area underneath it hasn't changed, so how can the pressure on the fixed area that mass acts against, change? I think you are adding the gas law to the study, when the study doesn't operate on that principle.