I've got a bad sense for these types of things. I recruiting agency hired me for a short term job (less than a month long). On the paper work I'm an employee of the agency. Their client is actually a managed IT firm. In actuality, I have almost nothing to do with the managed IT firm (or the recruiting agency) and I report to the manager at the managed IT firm's client and work at their site. Should I tell the recruiter this? I don't think she's actually very technical and knows what a managed IT firm is. Should I tell her that I'm basically a subcontractor? I don't really see this mattering to them and could only have the potential to cause a negative outcome.
To a headhunting recruiter, it depends.
To a Hiring Manager / HR Recruiter of the company, yes.
In the event if it's the second, for South East Asia (Singapore) it is recommended to clearly state both in your CV and in interview that you are hired by XXX Consulting Agency and was seconded to YYY company as IT/Engineering Consultant throughout the entirety of your previous employment.
Doing so helps to avoid any potential misunderstandings if the recruiting company runs a background check on you and found out that your payroll was under that agency which employs you.
Edit: Added Answer's country of origin for better context :)