The thing I most notice is when the temperature is below the co2 line the sunspots are also low.
For temperature driving CO2 I would point out a chemical reaction Nitrogen dioxide and Dinitrogen tetroxide. Those two gases are in equilibrium. If you change the concentration of one the other will follow. Proving A follows B does not disprove B follows A.
On that graph a temperature reading below CO2 levels that could not be explained by the sunspots would cause me to look for another explanation.
Another thing that would cause me to question the science would be a explanation for the less IR radiated by the earth in the bands that CO2 absorbs.