Possibly irrelevant/unnecessary addendum: ...since this is a randomly generated map.
I have discovered (from the American SG I'm currently playing, based on
@Marla_Singer's World Map.bix) that this is not necessarily true on prebuilt maps: the game doesn't always seem to register some of the visible river-sections (which will all have been placed by the map-creator).
On that particular map, many tiles which
appear to be adjacent to the Colorado, Rio Grande, Amazon, and the Rhine, don't actually give the freshwater bonus.