Can Atmospheric Pressure or Density Explain the Earth's Temperature?

In my last post , I responded to the claim that the greenhouse effect contradicts the second law of thermodynamics. When people make this claim, I often ask what it is that makes the Earth's temperature warmer than its effective temperature if there's no greenhouse effect. The response I get back usually has to do with what can only be described as an ill-informed, "crackpot" theory arguing that this is due to atmospheric pressure or density. Using the ideal gas law, critics of science calculate the temperatures on planets like Venus, Earth and Mars from other known quantities in the ideal gas law, and then assert that this means planetary temperature is due to density or pressure instead of GHGs. There are multiple versions of this, all of which claim either that there is no greenhouse effect or that the greenhouse effect has nothing to do with greenhouse gases and everything to do with atmospheric pressure and/or density. To my knowledge the original version of this...