The New York Times avoids making blanket statements about extreme weather events proving global warming. They simply give an extensive list of such events over the past year.
What’s true is that extreme weather events may indicate an increased probability of global warming. The probability is now high enough that we should act as if it is a certainty (which we should have over the last 30 years). However, it’s still a probability and a quieter 2013 won’t “prove” that global warming is incorrect.