Oracle 11G - Index Rebuild VS GATHER_TABLE_STATS
Gathering statistics and rebuilding indexes are two completely separate things.  


It is exceedingly rare that an index in Oracle needs to be rebuilt so any process that is regularly rebuilding an index is highly suspect.  I strongly suspect that rebuilding the indexes is unnecessary.  And I would strongly suggest spending some quality time reading through Richard Foote's Index Internals - Rebuilding the Truth to understand why rebuilding indexes is so rarely needed and those few cases where it is necessary.
You do need to gather statistics on tables and indexes when there are substantial changes in data volumes or distributions in order to give the optimizer the information it needs in order to determine the appropriate query plan.  If you create an index on an empty table and subsequently insert millions of rows into the table, you'll need to gather statistics to tell the optimizer that the table is no longer 1 empty extent.  Unless you disabled the automatic job, Oracle will also automatically gather statistics on any objects that have changed substantially since the last time statistics were gathered during the early morning hours every day.