To what page of search results do I have to skip to read something backing this claim of yours? Because frankly I got bored after reading 10 abstracts from the first page and no luck finding anything, but plenty of conclusions stating the opposite, such as:

Higher level of habitual physical activity is associated with a 31% risk reduction (hazard ratio 0.69, 95% CI 0.61–0.78, 6 studies, N = 557,487 individuals) of community-acquired infectious disease and 37% risk reduction (hazard ratio 0.64, 95% CI 0.59–0.70, 4 studies, N = 422,813 individuals) of infectious disease mortality.