Benignuman – I may not be using the term “midrash” correctly. I think that what I meant was “Midrash aggada”. I believe that people often use the term Midrash this way even though it may not be accurate. I admit to not being 100% clear on the precise terminology of divrei Chazal.
I do think that the Midrash that you referred to however, does in fact fall under the same category to which I was referring. I’m not sure why you think otherwise.