I have to agree with this. Security is the responsiblity of everyone in the organisation, from the helpdesk staff to the network programmers. It is the role of the security engineer to ensure that the organisation's security policy is being adhered to and to co-ordinate maintenance of network security, not to babysit staff and look over their shoulders while they work.
I don't agree with that. To be a good sysadmin, you must know both. If you aren't up to the task of learning both... you shouldn't have the job.