Note: this issue was unintentionally fixed in master/DXP with the inclusion of -
When attempting to view/edit the category of a child-site-scoped content, the field is not present if the category is that from the parent site. This is because the parent site(s) are not included when looking for possible categories.
1. Create a Parent Organization and site named Parent1
2. Create a Child Organization and site named Child1
3. Add a private page to the Parent1 Site
4. Add a category called "testCategory" to the "Topic" Vocabulary in Parent1
5. Update the view permission for the Topic vocabulary and testCategory category to be viewable by Site Member
6. Add an Asset Publisher to the page on Parent1
7. Configure the asset publisher so that it is scoped to Parent1 and Child1 and have it show content that contains all categories: "testCategory"
8. Through the Asset Publisher, create a web content article for the Parent1 Site and for the Child1 Site
9. Edit both articles
Expected Result: both articles should have testCategory category and it is viewable in the edit page.
Actual Result: Although both articles appear in the Asset Publisher and have the testCategory (viewable in the database), only the parent article has the field which shows this in the edit page.
Reproduced in 62x: 66bc5a1160ea8d7484de193f21d20b6271c60e23
Fixed in 70x: f24f159405ff329da1ce932f300136a13def8218
Fixed in master: 6b7a9af27efb0e143fe3b501665ce65a31a3756b