How will you enforce that they don't backfill one side and not the other, or how will you ensure in the future that one side is not excavated while the other remains backfilled?
You give no indication of actual height of everything. Is that a slab on the right side of the picture? If so, then this entire conversation is moot anyway.
I'm usually one to ignore contributions, in terms of support, when it's something that can be easily removed. I'd anticipate that at some point in the future they remove the backfill on the outside for whatever reason, waterproofing failure etc. Often this type of work gets completed without involving an engineer.
However, with the presence of the slab on the inside face, I'd be using that as a point of support. If in the future that needed to be removed for some reason, they'd better damn well be getting an engineer to look at it. So I'd be comfortable designing as if that is permanently in place. Then the contribution of the soil below the slab, from either side, is a relative non-issue design wise.
But maybe I'm missing something.