In an interview with IGN, Jason Jones stated that he enjoys playing Destiny with his 5-year-old son. I know that's it's possible for his son to have a tv, PlayStation or Xbox and the respective internet connection separate from that of Jason's, but I find that somewhat unlikely. The only other possibility possibility can think of is splitscreen. The point at which he says that is a little more than half way down the page. (I'm on a tablet so that may differ.)
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I hate to break it to you but Bungie and Activision have both confirmed that there will be no split screen gameplay in Destiny as it is a game for normal online multiplayer and they're making it like so, so players get the full graphical experience of the game. Sorry bud. No split screen.