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Alex D the rim bending inwards is actually caused by it being squishable together (when for example no spokes are used). Yeah, the spokes carry the weight through tension, but they carry it from the top, not from the bottom. Lacing the rim with many spokes gives it a certain stability, but the rim itself will still want to flex inwards, if thin enough (in the vertical dimension).
On the other hand, you can hardly make one diameter of a circle smaller without making the perpendicular diameter larger (making an oval), which means the spokes in other areas of the rim will try to prevent tis deformation...
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