Brian Williams showed why he’s well-liked by NBC colleagues the other day. He played third base for the “Nightly News” softball team as they were beaten by the “Today” squad 14-3 in DeWitt Clinton Park. When the thirsty players repaired to the back garden at Druids on 10th Avenue, Williams felt so bad for a couple whose romantic dinner was interrupted, he insisted on picking up their check. “He also paid for more than an hour of open bar for both teams, using a credit card, but tipped the waitress in cash — more than 30 percent,” said our spy. William McGowan, who was there celebrating his delivery of the final manuscript of his New York Times book, “Gray Lady Down,” said, “We talked about the journalistic importance of staying close to regular people, and [Williams] told me about dropping out of community college and also about being a volunteer fireman on the Jersey Shore. Total class act.”