I've received some big breaks by knowing the correct people, but not a single one of them has been a 2-minute connection from some BS networking event. It's always been a preexisting, unrelated relationship which eventually becomes career relevant.
I'm shocked by the number of seniors/recent grads who contact me out of the blue (god knows where they got my info) asking for recommendations or a break. No, I'm not going to stick my neck out by recommending someone I've never met for an open position.