How can I find a view column's base table column?

Three years later, the installed base of 11g instances out there likely moved to 12c just as we did.

OUT parameters don't have the same convenience as functions, but the WITH clause in 12c now accepts user-defined PL/SQL functions.

WITH
   FUNCTION get_expanded_sql_text_ (
      input_sql_text_ IN CLOB) RETURN CLOB
   IS
      output_sql_text_ CLOB;
   BEGIN
      dbms_utility.expand_sql_text (
         input_sql_text  => input_sql_text_,
         output_sql_text => output_sql_text_);
      RETURN output_sql_text_;
   END get_expanded_sql_text_;
SELECT get_expanded_sql_text_('SELECT SYSDATE FROM DUAL') AS expanded_sql_text
  FROM DUAL
/

Starting with 12c, we have DBMS_UTILITY.EXPAND_SQL_TEXT.

You basically pass the query text through the first, input parameter, and receive the rewritten query back through the second, output parameter.

But since you are on 11.2, you can not use this yet. You can however collect the optimizer trace. If you already ran your query, and have its sql_id:

begin
  dbms_sqldiag.dump_trace
  (
    p_sql_id=>'1a2b3c4d5e6f',
    p_child_number=>0,
    p_component=>'optimizer',
    p_file_id=>'optimzer_trace'
  );
end;
/

Or if you do not know the sql_id and did not run the query before:

alter session set events 'trace[rdbms.sql_optimizer.*]';
-- run your query here, no need to wait for results, it just need to be hard parsed
alter session set events 'trace[rdbms.sql_optimizer.*] off';

These will generate a trace file that you can read and find the final, rewritten query in it.

To be honest, the output produced by all methods can be difficult to read once you have some complex queries, and the way to get them is not so trivial, so I usually end up reading and "parsing" the DDL statements manually...

Do you have access to the execution plan? This will show how Oracle resolves view columns to base indexes or tables. You can create simple, dummy queries to focus on the particular items in which you're interested.