The authors recommend that the mentor not be a parent, even if the parent is qualified. For reasons of cost and convenience I am mentoring my kids.
Do they explain why they see it as being a problem?
From my perspective I think it is impossible to generalize about this sort of thing. For some parents and kids it could easily become a pressured unhealthy thing, but for others it could be a real joy. It certainly works out well for many homeschooling families.
The one thing I'd suggest with a mentor is that parents don't expect the mentor will cover the standard curriculum and they don't get overly involved in trying to guide the direction it will go.