Here's the key: "...the association was small and disappeared after the researchers controlled for characteristics of the child's family and early environment."
This does not invalidate the marshmallow test, it merely states that the child's family and early environment influence the child's later decisions, such as save/spend. They also influence the marshmallow test.
My thought too, by controlling for family and early environment influence and finding significantly less correlation, they are indicating that the results of the marshmallow test are not the cause of later decisions, it's merely correlated. But I didn't really think anyone thought that the marshmallow test caused later success, but rather it was an indicator of some other unidentified cause at play.