Think of it this way... you have a tree in the middle of a vast grassy plain. You want the tree to seem invisible, so you cover that tree with wrapping paper, that exactly mimics the grassy plain around it. However... the tree is still a physical obstacle, and when the sun's light shines on it, the shadow of the tree will still be cast.
If your cloak redirects the light properly then it doesn't merely 'cover' the object, but redirects light around it. A bright light shining on the cloaked object would illuminate the spot past the object where you would ordinarily see a shadow. At least in theory.
---------------
I absolutely get all of that. But you have to look at it this way... you are on the ground, looking up, at the Sun. Between your line of sight, and the Sun, is another object, say a ball, that has been "cloaked"... ok, fine. The light may be bent over all the surfaces of the ball, but from your point of view, you are looking at the Sun, with a physical object in the way... the light of the Sun covers a lot more area than a ball... we know this, because we squint, when we look towards the Sun, because the light/brightness increases. Therefore, the light of the Sun would extend beyond the surface area of the ball, and the ball would still cast a shadow on the ground, even though, by looking up, we may not see it (the ball).
Here is an example that may help... see this image below, of a forming solar system... now see the small planet that lies in the "Earth zone", in the dust belt. You see how it casts a shadow wake behind it, in the dust cloud? The same would happen if that small planet were invisible to us... it physically is still there, blocking the star's light, so the light of the star would have to go around it. Further, the dust around such a cloaked planet would also still appear to be displaced.
http://www.phys.ncku.edu.tw/~astrolab/mirrors/apod/image/0210/fomalhaut_atc.jpg
This is another reason why a cloaked plane might not work well. If it were to fly through either clouds or fog, it would give itself away, either by moisture forming upon its surfaces, or by displacing the cloud it's flying through, in much the same fashion as how Voyager caused the nebula cloud to move around it, as it flew through it, in the VOY opening credits.
Also, if it were to rain, the rain would be falling AROUND the object that is cloaked.