It so happens that I was also there and my memory of it is somewhat different of it that yours. He merely was using the notion of negative density as a mathematical tool to solve an unsymmetric problem, by subtracting a symmetric portion of problem (by way of negative density) to make the whole problem symmetric and then superimpose later that effect of what was removed earlier on to make the solution complete. This is something which is done routinely in other aspects of physics such as FFT, or in Complex mathematics.