That's really odd! You close C2 in between so there are no instances of C2 running, then open the second example, and the textures are wrong?
I can't imagine how that would happen, and I can't reproduce on my machine. Have you tried updating your graphics card drivers? C2 doesn't cache any textures between sessions like that (unless there's a weird bug), so all I can think of is a buggy driver is caching them.