This is in a Napili based Customer Community with a Customer Community license (not Plus).
The External Sharing Model is enabled and the Organization-Wide Defaults are set as follows:
Account, Contract and Asset
Default Internal Access : Public Read/Write
Default External Access : Private
Case
Default Internal Access : Public Read/Write
Default External Access : Private
There are no Sharing sets configured for this scenario.
The Community User Profile has Read and Edit access on both Accounts and Assets. The Community User Profile has Create, Read and Edit access on Cases. The Community User Profile has Read access on Contacts.
The Community is setup to have a Navigation link to a list page for the Cases, Accounts and Assets Objects.
When I go to the Cases page there are no Cases displayed and I would expect this since this Community User is not the Owner of any Cases. Cases are owned by Internal Users.
When I visit the Accounts page I see the Account listed that this user is a Contact on. The Community User is not the Owner of the Account. When I visit the Assets page I see the Assets listed that are on this users Account. The Community User is not the Owner of the Assets and Owner for Assets would be Controlled by the Parent in this setup anyway.
First confusing issue is why am I able to see the Account and Assets for this User at all if there is not a Sharing Set configured to display them and the Community User is not the Owner of either the Account or Assets.
Second Confusing issue is since I am able to see them why am I not able to Edit them? This Profile has Edit permissions on Account and Assets. When I am in a list view I can see the Pencil icon indicating the field is available for inline editing but get an access issue error if I try to edit the field. When I visit the Asset Detail page and click on the Edit Button (which is visible) I get a popup error message related to level of access. If I remove Edit permissions from both of these Objects the inline editing indicator icon and the Edit Button both go away.
The fields I am trying to Edit on either Account or Assets do have the Read Access and Edit Access boxes checked for the Community Users Profile.
I hope I have provided all of the details necessary and I am open to additional questions to assist in figuring this out.
Thank You