Either Marc Jacobs is being coy about picking up the bar tab for a friend’s birthday over the weekend, or someone signed his name on the bill as a joke. The fashion designer hung out at XVI in Midtown on Friday night with a friend named Christos till 2 a.m. But when another guest at the get-together went to pay the group’s bar tab, the wannabe big spender’s card was declined. According to the bar’s managers, Jacobs then stepped in and threw down his black American Express card to settle the $3,000 bill, which included charges for Grey Goose and Patron cocktails. But a rep for Jacobs denied he paid the tab, saying, “He didn’t even bring a credit card.”