Singularity just means that as element edge lengths tend toward zero, the stress tends toward infinity. In the example of the four nodes on the face of a hex element having a non-zero area, that is only true if the geometric area is maintained as the elements get smaller. For example if the edge length is cut in half, then the force is spread over 9 nodes to cover the same area as the original 4 nodes. If the edge length is cut in half again, now the force is spread over 25 nodes.
If the force remains on just 4 nodes, that would create a singularity because the force remains the same, but the area is tending toward zero.
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