Recently it has been suggested that multivariate analyses of functional magnetic resonance imaging (fMRI) data can detect high spatial frequency components of cortical signals, like sub-millimeter columns. This 'hyperacuity' seems to be at odds with the common assumption that the fMRI signal has a low spatial resolution due to the spatial spread of the underlying hemodynamic events. To resolve this apparent contradiction, I checked a very straightforward prediction of the hyperacuity hypothesis: if multivariate analyses are picking up a small-scale functional organization, then it can be expected that smoothing will be detrimental to the ability to decode these fine-scale spatial signals. I tested this prediction using data obtained with two paradigms to which multivariate techniques have been applied previously, including the decoding of grating orientation from the pattern of activity in primary visual cortex. It was found that smoothing does not decrease the sensitivity of multivariate analyses. Further simulations in which the scale of cortical organization was known indicate that this effect of smoothing contradicts the idea that the patterns detected with multivariate techniques reflect a fine-scale spatial organization.