In Oracle, what grants do I need as a non-schema user to view rows in all_objects?
Oracle data dictionary views that have the ALL_ prefix provide information about objects that your user has access to.  Views that have the DBA_ prefix provide information about all objects in the database.  And views that have the USER_ prefix provide information about objects that you own.

In this case, MYDBUSER does not and can not have privileges on the indexes owned by MYDBOWNER because there are no privileges one can grant on individual indexes so it makes sense that MYDBUSER would not see the indexes in ALL_OBJECTS.  If MYDBUSER were granted access to DBA_OBJECTS or DBA_INDEXES (either individually or via the SELECT ANY DICTIONARY privilege), you could query DBA_OBJECTS (or DBA_INDEXES) to get a list of all the indexes owned by MYDBOWNER.