I don't see why this is a problem. If the client wants a flat design with drop-shadows, than that's what he or she wants. Does that mean it won't be "flat"? Well, probably yeah. Should the client care? Nope. Was the objective (letting you know what he wants) accomplished? Yeah.
Whether the client should dictate this kind of stuff is a subject for another discussion.
Whether the client should dictate this kind of stuff is a subject for another discussion.