Whether true or not, the Pershing story may have stemmed from the Sepoy Rebellion in India in 1857. The troops, mostly hindu and muslim, were issued new Enfield Pattern 1853 rifles, using a paper cartridge, the end of which was bitten off by the soldier. The story was passed around that the grease used on the cartridge was from pigs or cattle. Of course, the musilms considered pork unclean, and the hindu revered the cow. Either source therefore was anathema. See this site for the result: http://forum.desicomments.com/showthread.php?t=12886

While the details differ from Pershing's alleged use of pig blood, the idea of uncleanness was the same. Stan