Dear Gil,
to avoid that someone gets a wrong impression: It holds in your situation that taking the correlation into account significantly reduces the computed probability for problems, but there are also situations such that ignoring the correlation reduces the computed probability for problems, see e.g. On the importance of accurate models of dependence in UQ: a cautionary tale.
Since your model is (as all models) a simplification of the reality, the computed settlement distribution determined by considering the probability distribution / set of samples with with correlation are only approximations for the values one has to expect in reality, and the same holds for the computed settlement distribution determined by considering the marginal densities. I think that the results determined with correlation should provide the better approximations, but there may be real world situations such that the other results provide better approximations of the reality. Hence, one may consider you considerations as the result of an ensemble computation / ensemble forecast using two sets of random variables as ensemblesand to perform afterwards a worst case analysis of the two results.