The hard part is over.
I'm matching you with one of our specialists who will be calling you in the next few minutes.
I'm not that familiar with the LTC policies, but I'm guessing that the issue of a private caregiver vs. an agency caregiver has to do with liability, since the insurance carrier will in the long run be paying for the services, and given that, has the right to establish some terms and requirements.
Back to the caregiving issue... let Mom know that if she hires someone out of an Agency she would need to provide an employment contract stating how many hours the caregiver works, what is that caregiver's salary, what days does the caregiver have off, and who will be paying the payroll taxes.
Another thing, it sounds like your Mom is living in her own home, if that is the case, then your Mom would need to get a "workman's comp" rider on her homeowner's insurance to help cover in case the caregiver gets injured on the job.
The above items is probably why the long-term-care insurance is asking questions. Someone outside an Agency might not be licensed, bonded, and insured.
Have Mom ask the Agency to send over some more people. It usually takes awhile to find someone who is a good match. And with 24 hour care, there is usually 3-shifts. So it won't be easy to find perfect matches in all 3 shifts. It is always a learning curve.