Quorly is a static page: plain HTML, CSS and JavaScript with no framework and no build step. When you write, the draft is stored in this browser — localStorage for the open document, IndexedDB for the library and its images. Nothing in that path is a network request.
The product's only server API lives under /api/, and it exists to answer two questions: what plan is this account on, and which features are switched on. It stores subscription state and feature flags. It has no document endpoint and no text field. You can read the shape of it in the privacy page.
That is what makes the claim structural rather than a promise. Adding an assistant would not be a setting; it would mean building a service that receives drafts, and that is a change large enough to show up in the network tab the first time you used it. The full data flow is written out on how Quorly works.