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The second paragraph is the reason why there will be no noticeable vertical flex in a wheel as long as the spokes are under tension. Unless the forces are so great that you overload the spokes, they will hold the rim in a precisely circular shape. The rim can never be anything else but round. If it tries to move towards the hub at one point, it simultaneously tries to move away from the hub at another point. Spokes prevent the second movement and therefore, by necessity prevent the first one.
Alex D is totally right, and anyone can simply test that for themselves, just as he described.
The only way to make a vertically compliant wheel is to use very few spokes. So few that the rim can deform substantially in the area between two spokes. For a variety of reasons this is not a good idea for offroad use.
And even if one were to build such a wheel, it is doubtful if such minor deflection would be noticeable against tire deformation, suspension movement, fork flex and handlebar flex, all of which are orders of magnitude larger than any possible deformation of the rim.
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