As for why the article mentions decreased lift whereas flaps down increases lift, that's maybe a bit more complicated. Lift vs. Angle Of Attack is a curve that tops out at about 15°.[0] Flaps often go to steeper angles than that, but I'm not sure if lift actually starts to decrease again in that scenario. Certainly adding a curve to the back of the wing (flaps) isn't quite the same as changing the angle of the entire wing.