Anyone ever have issues with HireRight background check not being able to verify past employers?

[BiscuitStripes, BSN, RN]

I've done background checks through them several times as well as other companies and have never had any problems until now.  This company was unable to verify several past employment records and they told me that I had to start doing the verifications myself by either obtaining the verification certifications or me calling the company and having the company call HireRight. 

The prospective employer wants the background check, they're paying HireRight, why should I be having to basically do my own background check.  This should not be my job.

Also, two of the hospitals I have worked with in the past require verification through a third party website, once of which charges $38.99 for a verification.  Why should I be held liable to pay for this verification when I'm not even the one requesting the background? 

I've reached out to HireRight multiple times and they've been useless, just go around in circles.  I've reached out to the Recruiter and am awaiting a response.  Has anyone else ever had problems with this company or similar problems with a different company?