I may be wrong, but it looks like pzErr message returned from xConnect call to an eponymous table is not propagated to the original caller, so the error message is "no such table: ..." even if my returned pzErr is not empty or null.
I'm not sure about my findings because pragma_table_info when called with invalid database (second parameter) reports another error ('unknown database') so this eponymous table is able somehow to report different errors.
I must admit that my wish to change it is a kind of exotic since from the very nature of eponymous tables (no parameters when created) they rarely should produce errors. But in my case I use the data from the database itself. Delaying errors for later (for example, cursor handling moment) is not possible because the schema depends on the data found.