For many, many years, we sold books through venues that allowed 3rd party sellers. This included Amaon, eBay, Alibris, Biblio, ABEbooks, GEMM, and many others. Most of that time, I subscribed to the services of FillZ who specialize in media (books, CDs, VHS, DVD, etc.) inventory management across all these venues, and it works flawlessly.
When something sold at Amazon, they would electronically pick up that sale, and delete that item, or reduce it's quantity on all other venues. We still got our "Sold - Ship Now" message. Nothing else was affected.
The technology for this has existed for many years, so if StitchLabs isn't able to do that, it's only a matter of time before they, or someone else can. And when they do, I'm jumping on board.