It's not "curve fitting", Am Fear. It is a brutal test to see if your model has the right physics, with the right choice of parameters.

And yes, through the accumulated efforts of thousands of scientists these models do a pretty damned good job of calculating the physicss of the atmosphere and how our climate has changed up to 2014, and how that climate will continue to change given different trajectories for CO2-levels.

Nothing is perfect, not even climate models. But they are good enough to be useful.