I haven't had a chance to read all the responses yet, so forgive me if this has already been posted.
As an instructor who also mentors, there are some considerations that must be taken into account. Agency standards dictate what we can do and even if we are not instructing we need to follow those. Some agencies allow instructors to take a diver one level above their current level of training if we are an instructor at that level, but standards apply such as ratios, visibility, etc. I will also not do this with someone I am not familiar with. In fact, I have only done this with some previous students. I also have my mentorees sign waivers as if they were in a course.
My reason for mentoring is to provide newer divers with an opportunity to learn something new and gain more experience. Courses are stressful and a student only learns so much. A mentoring dive allows a diver to learn more with less stress. This is one of the reasons I allow divers into my courses if I haven't met ratios yet.
I have also started doing mentorships days every couple/few months so divers can just come out and dive without paying an instructor fee. This isn't a class and won't result in a card, but hopefully it results in expanded knowledge and experience.
Edit - a little more now that I have read the thread.
I do not put my buddies or students into a trust me dive situation ever. But my definition of a trust me dive may be different. i consider a trust me div e as one in which a diver has to rely on someone else to get them to the surface alive. I teach my students how to do that on their own before we ever enter the overhead. Divers have died of heart attacks, strokes, and other things while under water. While I'm pretty healthy and have a physical done on a regular basis, what happens if I don't survive a dive?? I don't have a co-pilot to take over. My students have to know how to get out on their own, and I make sure I teach them this before we go in the overhead. I make sure they have the knowledge before the dive. They also have the right to call any dive at any time.
As for mentors v. instructors, the benefit some instructors have is exposure to several other instructors in preparation for their instructor status. This isn't true in all cases. Some instructors have only been exposed to one IT. My experience has exposed me to 9 different cave instructors so far. I don't necessarily agree with all of their teaching styles, but I have had the opportunity to experience it and choose what I think works the best. I think the same goes for non-instructor mentors. the more exposure to other divers, the more they can pass on.
I think instructor mentors are probably a little safer in that they do have agencies to answer to and so the information they pass on will at the very least be approved by a board of peers...hopefully. There is information I don't necessarily agree with in the student manuals. I still teach it, but I also talk about my issues with it and why I have issues. I then let me students/mentorees choose.
My advice is to get all the mentorship you want. Just be careful who you choose. I'm sure ev en Papa Bear has a mentoree or two out there ready to kneel on the cave floors in Mexico...