Please correct me if I'm wrong but what are we talking about here. There seems to be some confusion of terms.
First, lets take "Recruitment Agencies"
In Singapore, if I'm not mistaken, it's against the Employment Agency Act (Licensing) to charge prospective candidates fees to find them a job. 
This leads to the Agencies working for the Client Company who pays them to recruit certain employees. In short, they find people for jobs, not jobs for people. In order to do so and remain competitive I'm sure they do advertise bogus jobs in order to keep their databases up to date with fresh produce (the average local stays with any one company no more than 2 years). For your information, a check on MOM's website lists well over 1000 Licensed Agencies in Singapore. With this in mind, and the fact that some HR Departments send out Mass email requirements to dozens of agencies at a time (can't always get an exclusive - an most work on salvage rates "no cure - no fees") so speed is of utmost importance.
Now, look at Executive Search Services (Headhunters).
This seems to be where the bad press (Eepatwise) is ladled out. From what I gather, Headhunters generally are not interested in unemployed people (this is obviously a generalization if you are a contract type worker). This is where the term poaching arises in that industry. A client wants a specific type of person who is generally found at the client's competitor. Ethics won't allow them to directly approach their competitors staffs. This is where the Headhunter comes in.
He/she is generally a facilitator. If you send him/her your resume/CV and you are exceptional in your field, he'll keep you in his files. He may even market your CV to select clients in the hope of spurring them into action (good ones will).
"Headhunter"
confirming/clarifying my thoughts may be helpful.
Regarding the perceived racism here:
Racism is alive and well here.
Please don't get me wrong, when the advertisments say must be chinese speaking, it usually means the office generally is chinese speaking and would be more confortable with other chinese speaking employees. Or, their office may be in chinatown.
However, regardless of what the reasoning/logic given by the gov't, (i.e., communalism of the 60's). It's basically their way of forced integration. The HDB policy is a racist as it gets. The racial makeup of each block of flats must equal the racial makeup of singapore(If you think I'm kidding, look at the HDB for sale in the straits times classifieds - you will see ads that say open to all races, indian only, chinese only - that is why). Additionally, immigration (naturalization/citizenship) is also governed by the same statistical percentages. This is to ensure that the powers that be remain the powers that be. It is also funny because they have put so much emphasis on "education" but still do not give the citizens and credit. (I know...
let's not get into social moral/habits).
As one who was brought up in a racist family and who graduated school in the middle of the turbulent 60's in the US. I know what it's all about.
Manager
I also am in 100% agreement with your entire post.