Changing name of sql server (only default instance installed)

I need to rename a sql 2005 server and wonder about renaming the local groups created by the sql install (e.g. MACHINENAME\SQLServer2005MSFTEUser$MACHINENAME$MSSQLSERVER) to use the new name of the server. According to this URL I do not need to rename the groups:

http://social.msdn.microsoft.com/Forums/sqlserver/en-US/d69f171a-b857-41ab-bdff-5ad53abfb4e0/rename-machine-with-sql-server?forum=sqldatabaseengine

 
a. Is that correct?

b. If so, what is their purpose as they don't appear to be used?

TIA,

edm2