(currently studying Exercise Science at uni)
What we're currently being taught is that at lower-intensity exercise (walking), fat is the primary fuel used. Apparently muscles even prefer fat as a fuel, whilst the nervous system is the one that will take glucose or nothing. Anyway - as exercise intensity increases (eg running, or from a light jog to a spring) glucose takes over as the primary fuel. This being said, fat can also be converted to glucose, which helps explain why sprinters have low body fat ratios.
So, if running improves CV fitness as well by forcing the heart to work harder, why walk at all? Well, some people hate running, some people have bad knees, and some people have health conditions that screw up the conversion of non-glucose sources (eg fats and proteins) through the energy-production system, eg some thyroid disorders. Probably best to do what's safe for your body, and what you're likely to stick with for more than a day
Hope that helps!