I think you could posit two very different situations involving hiring a private DM.
The first goes back to the idea that you should really add one stress variable at a time to your diving. So you are a relatively new diver (and therefore all diving has an inherent degree of stress) and you are diving somewhere you have never been before, with conditions which may be different from where you trained. What you don't need is a buddy who is either a weak or novice diver himself, or a complete unknown to you, so you hedge your bets by obtaining an experienced buddy, who may be able to shoulder a bit more than the normal responsibility of a buddy. He may, for example, be able to manage most of the navigation, so that you can concentrate on your buoyancy and on staying together. I think is is a prudent behavior for an inexperienced diver, and an appropriate use of a DM.
The other situation is a diver whose skills are clearly insufficient for the proposed dive. The dive op suggests a private DM because they are worried that an accident or incident might occur, if this person is permitted to do their dives with a random or equally inexperienced/unskilled buddy. The onus on the DM is to try to prevent an accident that is already known to be high-risk. This is not good judgment on the part of the diver, the dive op, or the DM involved, but I suspect it happens. In this case, if the information we have is correct, the diver was judged to require that kind of assistance and refused it, and still went diving. If that is true, the outcome shouldn't surprise anybody.