Context. Gamma-ray burst (GRB) afterglows are excellent and sensitive probes of gas and dust in star-forming galaxies at all epochs. It has been posited that dust in the early Universe must be different from dust at lower redshifts. To date two reports in the literature directly support this contention, one of which is based on the spectral shape of the afterglow spectrum of GRB 050904 at z = 6.295. Aims. Here we reinvestigate the afterglow of GRB 050904 to understand cosmic dust at high redshift. We address the claimed evidence for unusual (supernova-origin) dust in its host galaxy by simultaneously examining the X-ray and optical/near-infrared spectrophotometric data of the afterglow. Methods. We derived the intrinsic spectral energy distribution (SED) of the afterglow at three different epochs, 0.47, 1.25, and 3.4 days after the burst. We reduced again the Swift X-ray data, the 1.25 days FORS2 z-Gunn photometric data, the spectroscopic and z -band photometric data at ∼3 days from the Subaru telescope, as well as the critical UKIRT Z-band photometry at 0.47 days, upon which the claim of dust detection largely relies. Results. We find no evidence of dust extinction in the SED at any time. We computed flux densities at λ rest = 1250 Å directly from the observed counts at all epochs. In the earliest epoch, 0.47 days, where the claim of dust is strongest, the Z-band suppression is found to be weaker (0.3 ± 0.2 mag) than previously reported and statistically insignificant (<1.5σ). Furthermore, we find that the photometry of this band is unstable and difficult to calibrate. Conclusions. From the afterglow SED we demonstrate that there is no evidence of dust extinction in GRB 050904 -the SED at all times can be reproduced without dust, and at 1.25 days in particular, significant extinction can be excluded, with A(3000 Å) < 0.27 mag at 95% confidence using the supernova-type extinction curve. We conclude that there is no evidence of any extinction in the afterglow of GRB 050904 and that the presence of supernova-origin dust in the host of GRB 050904 must be viewed skeptically.