Even 64-bit client is installed on computer,it persisted.Because it is required to install 32-bit as well.
The requirement of installing 32-bit client is about SSIS package installed on remote server is executed with 32-bit client.
SSIS package informations are folded in this link which is relating to SQL Server Integration Services
http://msdn.microsoft.com/en-us/library/ms141134.aspx
Shortly, simple solution is not to forget installing 32-bit oracle client on computer.
