well, good question, and a lot of it depends on the original OW training and one's comfort level.
BUT...........
I do remember being at a resort on a group dive of maybe 5 or 6 pairs of divers. The OWSI instructor gave the briefing and then said something like this--
be aware of your surroundings and of your buddy. You're all certified divers and this means you should be able to take care of yourself. If something happens and you can't get my attention immediately, don't wait for ME to take care of YOU....as divers, you are responsible for yourself and your buddy.
To me, basically, he was saying that with PROPER TRAINING, you should be able to dive without a DM or instructor at any time.....IF you are PROPERLY TRAINED!
I know there have been many threads going on about the alleged laxed training requirements of agency "XYZ" compared to the good old days, etc, etc....and that some consider it nothing more than "pay to dive and get your c-card". So, I am not sure if I answered your question or not.
For ME, if a DM or Instructor, or at least knowledgable diver is around, I like to go with them one the first dive at a NEW location. They can point out things on the dive and make it more enjoyable. Use their experience and expertise for this reason, but not because you expect them to save your butt when you screw up something at 60' depth.