It seems that melamine is not really added to the milk, but to the feed for animals. Melamine seems to be used as a contimination masking agent in animal feed. When impurities (mostly dirt) are added without melamine, protein tests can catch it. Adding melamine allows the "quality inspections" to pass, whether they are Chinese or American quality tests. The melamine seems to pass through the fluid paths of the body and doing a number on the kidneys in the process. Cows should have had this problem a long time ago, assuming that they have a similar physiology as human beings. The first time the problem was officially noticed was in dogs though.
Added later: As usual, the Chinese government is hanging some scapegoats. Continued vigilance will be needed to eliminate this and other forms of food contamination.