Sorry for the long post and lack of ascii diagrams.
OK I updated the wiki article to indicate that flowing into the sea actually counts as a dammed river.
I still have one more question, to all you experts out there. 
In diagram A of that article, it shows that the undammed river tiles to the left do not exert pressure because they are flowing. It then shows the one river tile to the right exerting a downward pressure to the tile below it. My question is, why does it exert this downward pressure? If this tile is flowing too, then wouldn't it fail to exert downward pressure, like the other flowing river tiles? Obviously this diagram is correct as experiments have shown, but does anyone have an idea as to why, given the game mechanics?
Understanding the diagrams is what allowed me to answer your questions. In diagram, A, the river itself is not considered pressurized because it has open space on the same z-level that water can teleport to without having to path upward. The tile at the right is only special because it has water below it, thus this tile is also not pressurized, but it is inducing pressure on the level below. The river itself does not need to be pressurized to generate pressure in water below it.
I'm pretty sure river source tiles behave exactly like screwpumps. Each tick they attempt teleport a 7/7 block of water into a square that probably already has 7/7 water in it. It first attempts to find a destination using down and sideways pathing trough other tiles that have 7/7 water. An undamed river always has enough space to fit enough water in near the downstream edge of the map. Failing that, it repeats the process allowing pathing up to the same level.
If you have a filled U-bend next to an undammed river, and the river will always teleport the water to the end of the river, and never to the top of the far-end of the u-bend. This is because the source tiles will always find a place to put the 7/7 water before needing to do the pathing check that includes upward movement. However, the mere existence if a u-bend means there is water over other water, and whenever this is true the water on top will attempt to find a home on the z-level below using any type of pathing (again, through other 7/7 water), although the game has some ways to avoid exhaustively doing this every tick.
Water being pumped/generated, water being physically above other water, and water spreading out to adjacent empty space (does not involve teleporting) are the only ways water moves.
Now, we accept diagram A to be correct. What is not covered by the diagrams is what happens if suddenly floodgates simultaneously dam the river
on both ends. Now we have standing 7/7 water on one side of the u-bend, with empty space on the other. Since we've also closed off the source tiles, no water is teleporting in, and so the 1-z level difference on each side of the u-bend will remain in equillibrium. This should be easy to confirm by making a very small u-bend and filling it with pond jobs on one side only.
Our notion of "pressure" is just what we observe of all this pathing and water teleporting. This is what the game is trying to model, after all, but its a result of what part of the algorithm the game is on, its not some monolithic variable that applies to some water but not other. For example, we think of pumps as always inducing pressure, but the rivers show us that pumps will not induce pressure as long as there is sufficient room on the same z-level or z-levels reachable through sideways and downward pathing only.
Magma is identical except the 'falling' rule never causes it to path upward ever. I have no idea how any of this applies to the magma sea, semi-molten-rock, or if map-edge tiles that are by-default submerged behave like river-sources (I think they just count as permanent 7/7 water and water flows from them only when the edges themselves are below 7/7).
Another interesting experiment would be to pump into a closed u-bend with the pump outputting on z0. If you put a long corridor on the far side of z-1, then water should reach z0 on the far side before reaching the end of the z-1 corridor. I think this would be so because the pumped water will be in pressurized mode "path anywhere," and it should choose the shortest path even if a longer but lower path is available. Then repeat the experiment but with a long corridor on the
close side of z-1 (with infinite drainage/map edge at the end). In this case the water will never crawl up the far side of the u-bend, because it will always find a destination before moving into 'path upward' mode. I think I can be pretty confident about the second test, the first one is a bit more murky, and would tell is if water tries to find teh shortest path, or if it exhaustively searches each z-level before moving upward again.
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Topic: Why is this flooding happening? (Read 16520 times)