So it sounds like people ask about this because they wonder if the applicant has been mistreated by a bad agency.
Our prospective nanny did use an agency I believe, but it was an agency that had assisted her sister and a couple of her friends to come to Canada in the last couple of years, so I think she felt confident that the agency was a good one. I think she used an agency because she was working 6 full days per week, with only Sundays off, and very long hours so it would have been very difficult for her to do the application all by herself. She told me she was not charged too much, because the agency gives a big discount if you already have a Canadian employer and LMO/LMIA when you hire the agency.
I don't think the agency made any mistakes in our case. I contacted my Member of Parliament a few weeks ago, to see if he could help us, and his office contacted the HK embassy for us. The embassy confirmed that they had our nanny's application and that there was nothing missing, incomplete, etc. So we know the application was for sure submitted correctly back in April. The embassy gave us an estimated processing date of September 22 (5 months from the date she applied). Now we are just waiting, and hoping she has her Visa by the end of September.