Kathleen,
Skim cows milk goes bad faster because it is more processed, allowing more
degradation and greater possibility of contamination.  In nature, untampered
with, high fat foods spoil more quickly, as the fats go rancid.  Compare whole
wheat flour and white flour.  That "off" smell in stale whole grain flour or
rice is rancid fat.  This is why birds eat high fat fruits very quickly when
they ripen in the fall, before they spoil, leaving lower fat food sources to
be utilized later in the season.  So Dr. Lawrence's assertion makes perfect
sense in light of these tidbits.
Catherine Watson Genna, IBCLC