Fairall 9 is one of several type 1 active galactic nuclei for which it has been claimed that the angular momentum (or spin) of the supermassive black hole can be robustly measured, using the Fe Kα emission line and Compton-reflection continuum in the X-ray spectrum. The method rests upon the interpretation of the Fe Kα line profile and associated Compton-reflection continuum in terms of relativistic broadening in the strong gravity regime in the innermost regions of an accretion disc, within a few gravitational radii of the black hole. Here, we re-examine a Suzaku X-ray spectrum of Fairall 9 and show that a face-on toroidal X-ray reprocessor model involving only nonrelativistic and mundane physics provides an excellent fit to the data. The Fe Kα line emission and Compton reflection continuum are calculated self-consistently, the iron abundance is solar, and an equatorial column density of ∼ 10 24 cm −2 is inferred. In this scenario, neither the Fe Kα line, nor the Compton-reflection continuum provide any information on the black-hole spin. Whereas previous analyses have assumed an infinite column density for the distant-matter reprocessor, the shape of the reflection spectrum from matter with a finite column density eliminates the need for a relativistically broadened Fe Kα line. We find a 90 per cent confidence range in the Fe Kα line FWHM of 1895-6205 km s −1 , corresponding to a distance of ∼ 3100 to 33, 380 gravitational radii from the black hole, or 0.015-0.49 pc for a black-hole mass of ∼ 1 − 3 × 10 8 M ⊙ .