How Can a firm charge a client for hiring me if I am not their employee, nor have a non compete contract.

Question

I currently obtain part time shifts through a company that declares I am not an employee, I am an independent contractor. Therefor they can not and will not verify that I work through them. One of the facilities I have been providing assistance to wanted to hire me FT. I was interested.  They say they have no signed contract with this firm. 
Now I can not have the job because this company tells the prospective employer the following: 
 I spoke with our representative at Medely about a hypothetical situation wherein we would want to hire one of their agency personnel that had worked here at FASC. What I was told was that there is a 2 year term during which we would not use the person before the Opt Out fee does not apply.  Next, their fee is 18% of the person’s 1st year salary.  This is very steep and would not be feasible for FASC at this time.

Bruce Alexander Minnick · Answer

If you did not sign any documents or a contract with the employment agency I would be very surprised--because all of them require people like you to do so.  
 
Moreover, if an employment agency or company has been sending you out to work at various places then you can be sure the agency has some sort of contractual relationship with every employer they send you to.  
 
So: Unless you are paying the agency yourself--all the employers that hire you are paying the agency some kind of fee for finding you and sending you to them. That is the way employment agencies make their money.  
 
Most employment agencies use contracts that warn the employer NOT to hire you away--and not to hire any others they send--without paying the agency some additional "finders fees." That is probably what is happening here.

Q: How Can a firm charge a client for hiring me if I am not their employee, nor have a non compete contract.