Running a SSIS Package from SQL Server Agent Using a Proxy Account

When we try to execute a SSIS package from a SQL Server Agent job it fails with the message "Non-SysAdmins have been denied permission to run DTS Execution job steps without a proxy account." if the account under which SQL Server Agent Service is running and the job owner is not a sysadmin on the box or the job step is not set to run under a proxy account associated with the SSIS subsystem. What is this exception about? What causes it and how do I resolve it? For more details, click here.