I am no expert, but I always assumed that the close proximity to such a diseased person would only slightly increase the risk of infection; after all, we are ~250 persons sitting in close proximity in a small, confined area with air circulating all around us, and therefore even if the person sitting two rows in front of us, or across the isle, or behind us, starts sneezing, we are inevitably going to inhale [or come in contact with] its contents.
But yes, I too naively use the wet towel they provide to disperse & spread all existing germs around the pull-out trays, arm rests, and my face and hands, believing it is somehow going to protect me from getting whatever disease the person had who was sitting in the same seat on the previous flight; or from the FAs for that matter.
Since I pretty much consider the inside of any plane to be cesspool-like, I now follow these two simple and very related principles:
1) As regular flyers we are building up an extremely strong immunity through light exposure.
2) What won't kill you, will make you stronger.
Added: As an aside: the "infected" person in OPs post might have only been suffering from hayfever!