How can intelligence not play a factor!? How do you think Hashirama, Minato, Itachi, Sasuke, and even Madara were extremely powerful people: They are very smart and analytical people (obviously there are more).
Prime example: Nara Shikamaru
In his fights against Temari, Hidan and Tayuya...he was clearly outmatched combat wise so how did he survive?! Because he's extremely smart. It takes intelligence to both focus, plan, and analyze when in combat. If one doesn't hold any degree of intelligence, they will not be able to effectively use their strengths in ways to achieve victory. Nor would they be able to predict how someone will try to move in on your weakness.
But Shikamaru also shows the degree of proof to your argument.
He is not by far near the strongest shinobi to exist. Naruto, Kakashi, Neji, Lee, Madara, Sasuke and anyone you can fit in a top 30 list beat him solidly. However, Shikamaru is able to live combat with these people around because he was able to think.
For example: he lived through Hidan and Kakuzu while playing a significant role. He even managed to save Kakuzu. During the war he managed to catch Obito into a trap in which Obito was saddened that Shikamaru was a threat. Sending the Gedo Mazo to kill him.
Had he had the stamina/time, Shikamaru may have been able to use shadow stitching to hold Obito down....
Intelligence plays a key role in battles, but clearly there are other factors.