Note I cranked the base Mud penalty up to +4; minor rivers are now +1, major rivers +2.
[Two different movement options superimposed on the same unit note]

The tank in both cases is moving into a Field tile, outside of any Zones of Control, and the tank isn't moving from a road hex to a road hex (which in Mud doesn't matter anyway). The ONLY difference between the two tiles would be that river to the SE, which the tank isn't even crossing. So why would the river reduce movement costs by 3 on its own? Wouldn't the river possibly be at flood stage in muddy conditions?
The +4 penalty I noticed only applies to flat tiles with no trees; non flat/open hexes simply apply an additional +1 penalty in Mud, which since they already are +1 or higher for the base terrain penalties it isn't a big deal.