What was studied in both articles linked to is not what is usually meant by those who talk about the power of positive thinking. As others have pointed out the idea behind the power of positive thinking is imagining successfully completing the goal, not imagining having successfully completing the goal.
I am a fencer. One of the people I fence with often says before they fence someone, "I can't beat them. I am a terrible fencer." Unsurprisingly, after saying this they usually lose, even against people I have fenced and know they are better than. Occasionally, they will be convinced that they are not a bad fencer. They will enter a bout against someone convinced that they can win. When that happens, they usually win, even against fencers I know are better than they are. Positive thinking does not cause them to beat fencers who are a lot better than they are, but it, sometimes, allows them to take advantage when those fencers underestimates them.