I think they routinely close the doors 10-15 minutes prior to departure time. It would seem better to me to close them at listed departure time, then take off after that, but there is probly some scheduling rule that makes this so.
Edit: I found it on Contract of Carriage, which we agree to - read or not - when we purchase a ticket, but I remember it only because it's also printed on the boarding passes...
One could argue that it wasn't his fault that his inbound plane with the same airline was late, but it was not the airline's either - as he said, it was delayed because of rain. In inclement weather, landing intervals are increased for safety. Ok, so they told him that they would hold the connecting plane? I'm sure that they try, but the person offering that assurance had no idea what the various complications may have been, next plane needing that gate, inclement weather turning worse so the pilot felt compelled to get gone while he could, etc.
So yeah, it was luck of the draw, with weather calling the hand. I've been thru worse a few dozen times since the 1960s.