A company that is truly a "professional staffing agency" is not a temp agency. Just as you say. So I wasn't referring to you.
There are "staffing agencies", and there are temp agencies. You know who you are. If you are not one, then I wasn't talking about you, was I?
I do agree about establishing a relationship with firms, and that is a motivation. But not all agencies -- and not all employers for that matter -- are looking for "permanent" solutions.