The knowledge of IR absorption spectra is not used only in climate science, and the climates science is not the first major application and motivation for the related computer codes. They were developed for remote sensing and reconnaissance applications on both military an civil sides All these uses verify the accuracy of much of the data.
The data and the models are also verified by the measurements of downwelling IR radiation at surface and satellite observations of IR radiation to space.
I cannot provide any specific references, but the understanding of the mechanisms and the correctness of the data has certainly been validated in many different ways both by laboratory measurements and by observing real atmosphere.