In order for the user to update that page, they will have to have access to all pages above it in the tree. The usual method is to give them access to the page itself with a Policy that allows editing (e.g., ContentEditor), and give them access to the pages above it with a policy of Load, List, and View. Load only might work but I don't think so.
You might also consider NewsPublisher. That would let the user log in in the front end and edit pages. Keeping them out of the Manager makes things a lot simpler.
If the user is the original author of the page, or could be set as the author, it would be even easier. This tag on the page itself (or in its template), would show the user an "Edit" button on that page alone that would launch NewsPublisher and let them edit the page:
[[!NpEditThisbutton &ownpagesonly=`1`]]