First off, the original article is open access at PLOS ONE here: http://www.plosone.org/article...
The summary statement, "The tip of the olfactory nerve, which contains the smell receptors, is the only part of the human nervous system that is continuously regenerated by stem cells", implies several things that are misleading and/or totally untrue.
The tip of the olfactory nerve is the olfactory epithelium, where the olfactory sensory receptor cells are located. The olfactory nerve travels through the cribriform plate, a porous area of skull, where it then synapses with the olfactory bulb. The olfactory bulb has several cell types, and only one of these, inhibitory granule cells, is continually regenerated via neuroblasts migrating along the rostral migratory stream from the sides of the lateral ventricles. These cells are thought to play a role in associative learning and coding of new olfactory cues. The olfactory nerve does not have a capacity for self-renewal, nor do any of the olfactory receptor cells.
Furthermore, there is more than one area where neurons undergo continual self-renewal. The dentate gyrus of the hippocampus also fosters a neurogenic niche, and these new cells have important implications for learning, memory, stress, and emotion that we are just beginning to understand.
Thirdly, we don't really know if neurogenesis in the olfactory bulb has anything at all to do with the observed results because this was not measured in the study, but it is a plausible hypothesis for future study.
As a side note, one of the very intriguing aspects of neurogenesis is that after cortical injuries such as trauma or stroke, neuroblasts from the ventricles migrate toward the lesion, rather than toward the olfactory bulb. These cells are capable of forming electrochemically active synapses at the lesion site and appear to aid in recovery. Unfortunately, astrocytic scarring and inflammation limit the regenerative capacity of these cells - but this is an area of intense research in the field of neurotrauma. My current (undergraduate) research is focused on analyzing the effects of post-injury recovery environment (for rats) on subventricular and hippocampal neurogenesis.
For a good summary on neurogenesis: