They claim that this is perhaps down to dopaminergic neuron toxicity being attenuated and weakened by the administration of caffeine, at least in mice.
A couple of studies were run investigating the temporal onset of protection and what was found is quite interesting;
Study 1 - Pre-MPTP
The first study investigated giving caffeine (30mg) 10 minutes, 30 minutes, 1 hour and 2 hours before an MPTP (Methylphenyltetrahydropyridine - a known neuro toxin related to Parkinson's disease) injection and found that caffeine greatly attenuated toxicity induced striatal dopamine depletion. Caffeine was also trialled 6 hours before the treatment but did not attenuate toxicity.
Study 2 - Post-MPTP
The second study looked at a second group of mice who had not been given caffeine prior to MPTP injections but were given caffeine after MPTP injections. The results here also showed similar attenuation but only if given up to 2 hours after and did not weaken toxicity after this point.
These results show that caffeine does have a neuroprotective effect in the MPTP model of Parkinson's disease, at least in mice. It would be incredibly interesting to see this replicated on a human sample to investigate further.
Xu, K., Xu, Y., Chen, J., & Schwarzschild, M. (2010). NEUROPROTECTION BY CAFFEINE: TIME COURSE AND ROLE OF ITS METABOLITES IN THE MPTP MODEL OF PARKINSON’S. Neuroscience, (167), 475-481.