Spinal tap got it right: d minor is the saddest key. I think Reiner was riffing on christian Schubart, from google:

“D minor, wrote Schubart, is a key of “melancholy womanliness, the spleen and humours brood.” He actually found D#minor to be sadder. It is the key, he wrote “of brooding despair, of blackest depresssion, of the most gloomy condition of the soul.”