Stock browser does not allow access to files from local storage (e.g. "file:///" protocol) - this is security feature (and a standard thing for Android).
I do not know what exactly app you are pointing to is doing - however on Sony PRS there are actually 3 browsers:
1. Standard one from Google - never visible and I am not sure how to open it. Chances are however that this is the browser your app is trying to use - since it was not written for Sony.
2. Sony modified browser - the one you actually see (with paging).
3. Another Sony modification used when opening Sony Reader store.
Your best bet to read html files would be to use some application on PC and convert them in supported e-book format (epub?)...