Mitering can mean a weaker seam at the edge. If you've got a sharp edge, it will be very thin where the two pieces meet. If you hide the miter with something like an ogee, (which is a weaker edge also) then it's a bit stronger, but not as strong as a plain square laminated edge. So yeah, a mitered seam is weaker.

A triple laminated edge isn't going to look that great in most granite though. It's best done in something like a quartz that doesn't have any movement that will make the seam more obvious. Your desired look seems to be at a bit cross purposes to what can actually be done in natural stone, as well as what will be durable in natural stone.

If you were willing to sign the waiver accepting the responsibility of the potential breakage, after the fabricator explained all of this to you, then you should have gotten whatever you were willing to pay the upcharge for. If you weren't willing to assume the responsibility for going against your fabricator's recommendations, or pay him extra for him to assume the risk, then you weren't being reasonable in your requests. Someone has to assume the risk, and it doesn't come at no additional costs to the job.