The suggested normalization procedure, even with the ad-hoc fix for gradient discontinuities, doesn't actually ensure that the resulting function is 1-Lipschitz unless the gradient of the gradient magnitude vanishes. The signed-distance functions considered in the article seem to have piecewise constant gradient magnitudes (so are L-Lipschitz, just with L > 1) except for inside the "r", but for less well-behaved functions, higher order derivatives might start to matter.
Sure, but signed distance fields by definition have a constant gradient magnitude, aren't they? They measure the distance from the surface, which grows linearly in the normal direction.
But it is true that general implicit surfaces don't necessarily have constant magnitude gradients. I.e. F(x,y) = x^2 + y^2 - 1 vs. F(x,y) = sqrt(x^2 + y^2) - 1
