Sorry guys, but I don't understand where the problem is.
Swamps don't block supply because swamps can be accessed by wheels.
For example, on dry ground, it takes all the movement points (= "MP" in the following message) of the wheeled unit to move in a swamp. Just point your mouse on the "i", and it will show you the MP cost for this hex concerning all types of transport.

- marais - 2.jpg (332.57 KiB) Viewed 1625 times
("Sur roues" means "wheeled" and "tout" means "all")
The best way to check if a hex blocks supply is to check its attribute. For example, a lake blocks supply, as shown in the following screenshot.

- lake .gif (487.42 KiB) Viewed 1625 times
And you can see that the blocking supply attribute doesn't appear on a swamp hex.
So, the manual is correct and is not misleading in any way.
All the screenshots you took doesn't prove the contrary. It's just that you're misunderstanding what they are showing.
For example, in your 1st screenshot, the fact that the infantry can move into the swamp hex without abandoning truck does prove that swamps can be accessed by wheel. The movement will cost all the MP of the truck. So, with its truck, the unit can't go further north. However, moving into the swamp only costs 2 MP of the infantry (using its feet). So, the unit still has 1 infantry MP, which means it can go 1 hex further north, but at the cost of abandoning its truck.
Of course, going around the swamp is off limit by feet (only 3 MP = 3 hex) or by truck (8 MP = 4 hex because no road).
You have to remember that when a unit has an organic transport (like a truck), the game will always check that the movement you're trying to make (without transport) can also be made by the transport. Otherwise, the unit has to abandon its transport.
- Movement within range of native unit and transport = no problem, movement made without using transport
- Movement off limit of native unit but within range of transport = movement made using the transport (and there is an additional rule which allows the unit to disembark at the end of its movement if it doesn't use too many MP of the transport MP)
- Movement within range of native unit but off limit of transport range = movement allowed if transport is abandoned
- Movement off limit of native unit and transport = movement not allowed