Turns out that he cultivated that impression very assiduously. More recent scholarship has shown that Ike was in fact very engaged, especially (and naturally) on the foreign policy side of things. And very wily, too.
As a fan of Senator Robert A. Taft (R-Ohio), I'm not the most enthusiastic Eisenhower enthusiast. Nonetheless, Ike's accomplishments as president include terminating the Korean War, reforming labor union practices, modernizing our strategic defense and intelligence capabilities, tossing the Reds out of Guatemala, and starting us on the road to the moon.