I have Crohn's disease, have therefore been exposed to numerous doubtful stories about 'boosting the immune' system. With my illness, a 'boost' would actually make me sicker, whereas I find that fasting for a couple of days results in improvement of symptoms for me. Why? Obviously because my digestive system becomes empty, and there is less irritation of damaged intestinal lining. Going by this study, an increased production of white blood cells should make me sicker. My anecdotal evidence does not support their findings.
Long story short - if their claims are true they will be able to be reproduced by other researchers. Until then, colour me sceptical.