Maybe this hints at the actual mechanism we should focus on, rather than "rain":
"In total, 1492 samples comprising of water, leaf and fecal matter were collected for the analysis."
I've read people saying they drive past commercial fields with workers taking a dump right in the field.
Any home gardeners who do that should not harvest right after rain!
Or, if the fields were recently manured with raw manure, I would hope they would have mentioned that in the paper! But I think there are federal regs about how long you have to compost before applying manure.
Having mulch under leafy crops always sounded smart to me.