My thought is that you build it the best you can with the constraints that you've been given. I think you've done your best to advise of potential pitfalls. I hate to say it, but if something does happen with it, you can redo it, but certainly not under a warranty status. You can then add the back or supports or whatever is required, I'm sure with a lot less resistance.
Remember, the customer is always right, until they aren't.