One more interesting finding.
Gutenberg editor uses RESTful API to fetch the list of pages for "Page Attributes". If you are using AAM UI to manage access to Pages on Posts & Terms tab, then make sure that you also check access settings on the "API Access Settings" section.
I'm currently working on AAM v6 that consolidates all access settings in one list. So there will be no more separation between "Frontend", "Backend" and "API". This is due to the fact that RESTful API is completely blurring the border-line between frontend and backend.