Matehmatically you are right but logically wrong. The Col. is referring to the beginning of the 60th year of independence and the culmination of the 59th on Janmaashtami -- it nicely fits into the philosophy of no beginning and end, isn't it?
Don't subtract, include! Then it becomes 60. If the first independence *day* is Aug 15, 1947, then certainly Aug 15, 2006 is the 60th. It's independence day, not year. Next year will actually mark 60 years of independence, though the day will be the 61st.