"That's not a demonstration that it's not happening."
I'm afraid it is.
"Attacks on the credibility of existing models do not automatically make alternative models better."
Not quoting any alternative models , just empirical data , you know, what you say your looking for.
Back in 2007 , IPCC AR4 models of past atmosphere , according to there understanding ,had a hot spot at the equator (1890 to 1999).It was only suppose to get hotter according to model forcasts. 
see: www.ipcc.ch/publications_and_data/ar4/wg1/en/ch9s9-2-2.html
9.2.2 Spatial and Temporal Patterns of the Response to Different Forcings and their Uncertainties
That's what the satellite data from RSS & UAH are showing for the lower troposphere
If there is no increase in warming in the atmosphere, then whatever is being shown at the surface has nothing to do with increasing atmospheric CO2 .Although the planet is getting greener.