Your statement is utterly false simply by virtue of the documentation.
Inserts never propagate to other tables in a hierarchy
Indexes/Constraints only apply to individual tables
Since inserts do not propagate the base table never sees the records and thus the index on the base table cannot enforce uniqueness.
Other caveats and restrictions to the current inheritance implementation can be found in section 5.8 (Inheritance) of the documentation. It is in the “Data Definition” chapter.