"Previously, researches have found that fluoxetine (Prozac) actually suppresses neuronal growth in vitro"
Neurogenesis is only one type of plasticity, and it doesn't sound like the type they're talking about in this article. (Albeit I didn't read the study.)
While they didn't measure neurogenesis directly in the study, they did measure BDNF (Brain-derived neurotrophic factor) which can induce neuron growth[1]. Essentially they took two groups of mice: regular mice, and mice whose BDNF levels are believed to not respond to Prozac (Flx). They found that in regular mice, Prozac plus retraining reduced anxiety. In those mice in which Prozac doesn't increase BDNF, the Prozac effect went away.[2]
I know it's hard to read the actual study all the time, but sometimes it helps. :)
[2]Because mice heterozygous for the BDNF null allele (BDNF+/−) are insensitive to Flx treatment in behavioral models of depression and anxiety (3, 26), we tested whether BDNF+/− mice (C57Bl/6J background) responded differentially to Flx in the fear-conditioning paradigm. Flx again prevented fear renewal in the wild-type mice, but in BDNF+/− littermates trained to fully extinguish the fear response, the Flx effect was absent as indicated by elevated levels of freezing 1 week after extinction (Fig. 4B and fig. S7). To test whether BDNF was acting predominately in the amygdala, we used doxycycline-regulatable lentiviral infection to overexpress BDNF locally in the BLA from the end of extinction onward (figs. S8 and S9). BDNF-overexpressing mice did not show fear renewal, whereas control mice did (Fig. 4C).
Neurogenesis is only one type of plasticity, and it doesn't sound like the type they're talking about in this article. (Albeit I didn't read the study.)