The article is still extremely vague and unenlightening. It mentions duties, but, with the exception of the line producer, does not really specify what those duties are.
At the low/no/mini/micro budget indie level there are "money" producers and "hands-on" producers. "Money" producers will put up some capital. "Hands-on" producers are essentially line producers, and are the 1st ACs alter ego; they are the directors off-set buffer/organizer the way the AC is the on-set buffer/organizer; at least that's how it is supposed to work.
I occasionally work with an indie producer who, at least in my opinion, is a great indie producer. I'm not privy to everything that she does (fund-raising, budgeting, etc.), but she's terrific at the working level. Her job is, as she describes it, to serve the director and the directors vision, to keep the project on time and on budget, and to keep everyone involved happy and motivated. All I know is that working on her projects is fun, I'll work with good people whether they are long-time pros or newbs, and that I'm going to eat really well. A happy crew and cast will work hard, and she gets everyone to put out 1,000%