Each line is the path traced by a water molecule (layman's explanation, please correct me). DSI is a variant of MRI that seems to have been developed precisely to map small crossing fibers, so that would be a huge failure.
[1] http://en.wikipedia.org/wiki/Diffusion_MRI [2] http://www.technologyreview.com/news/410560/the-brain-unmask...
The problem is not the tool, but the statistical analysis of the data, which depends on a lot of parameters, and the number of different gradient directions, which are usually orthogonal, hence favouring orthogonal neuronal connections and discounting those that are diagonal to the gradient directions. You have to correct for this in the analysis, but it's very hard to do, and mostly guesswork. Which coincides my personal evaluation of the entire study: guesswork.