100% agreed - that's what I learned to do in high school journalism class as well. But there's lots of stuff on the web, even that's considered news, that doesn't follow this format. Here's some first sentences from other Times articles:
"The flesh is weak but the spirit of commerce is willing." (op-ed)
"Last weekend, my family and I packed our car full of supplies and drove to a fire station in New Jersey to deliver goods to an area that had been hit hard by Hurricane Sandy." (small business)
"Last April 28, a splendid spring Saturday that fairly begged you to be outdoors, I spent all afternoon in front of my living-room TV, anxiously watching the last day of the annual N.F.L. draft, live from Radio City Music Hall. " (NY Times Magazine)
"The relocation of Albert C. Barnes’s great polyglot art collection to central Philadelphia was opposed by many and dreaded by most." (A&E)
I guess my point is that journalism styles vary even within a publication. Therefore, any automated attempt to simply use the first paragraph as a summary is bound to be wrong a lot of the time. It would however be interesting to use a human-generated summary dataset as the training data for a "buries the lead" classifier. I'll bet you could do it with a bag-of-words feature pretty easily, and that the most important words would be personal pronouns.