The Ghillie suit and hood do not alter the shadow of my character, they only show the outlines of the character without it.

In the screenshot I added you should be able to see the outline of the shadow in the background.
In case that this screenshot is not clear enough, here's a link to another screenshot I made and uploaded to the steamcloud.
http://steamcommunity.com/sharedfiles/filedetails/?id=375566798

Shadows are set to normal, GPU is an AMD r9 280, the drivers are up to date.