The "rotation" model shown at the top of this artist's illustration held that the iron feature was being spread out by distorting effects caused by the immense gravity of the black hole. If this model were correct, then the amount of distortion seen in the iron feature should reveal the spin rate of the black hole.
The alternate model held that obscuring clouds lying near the black hole were making the iron line appear artificially distorted. If this model were correct, the data could not be used to measure black hole spin.
With NuSTAR's data, the alternate "obscuring cloud" theory has been ruled out. High-energy X-ray data -- shown at top as a green bump to the right of the peak -- revealed that features in the X-ray spectrum are in fact coming from the accretion disk and not distorted by the obscuring clouds.
These space observatories were able to make the first conclusive measurement of a black hole's spin rate and confirm that the "gravitational distortion" model is indeed accurate.