Little more detail?
Can you give a little more detail? Sounds like you are maybe the GC and this is new construction, so I'll answer in a couple ways.
First, "no squeaks" is never a guarantee from whoever installs the floor. Squeaks are usually because of framing where a nail has missed a joist and is rubbing, loose subfloor rubbing each other, broken tongues in T&G subfloor, incorrect nails used which have backed out, etc. Squeaks usually don't come from the finished floor, but from the subfloor. Thus, screw, and maybe glue as well, rather than nail subfloor.
One of my installer handbooks doesn't discuss this specifically, just says minimum required is 3/4" plywood or OSB (no particle board). Could be two layers, could be one, whatever, as long as total thickness is at least 3/4".
If this is a remodel and you aren't doing the joists and subfloor, you may want to consider putting down a second layer of subfloor. The second layer gives it strength, turn it 90 degrees to the first subfloor. If the floor is SOLID, my bigger concern is being level. No rolls or dips, no having a joist with a noticable crown turned up, etc. May have an issue with matching the height of floors in adjacent rooms, case work, and doors.
If you are the GC, when you do the joists try running a stright edge over them and look for crowns causing "bulges," etc., before doing the subfloor. Lot of people like T&G such as Adventek on the subfloor, glued and screwed. Personally, I'm ambivalent about the glueing and the Adventek because if you ever have to take any of it up there is major pain from the glue. Makes for a really good installation, but you are saying any future problems are too bad for whoever fixes any future issues.
I'd just as soon do two layers of square edge 3/4" B/C plywood, screwed, and the second layer done at 90 degrees to the first. I'd run the first layer to the edge of your framing and set the studded wall on top of it; the second layer would be "inside" from studded wall to studded wall. If it ever has to come up hopefully it only means the top layer has to be replaced. And two layers really give a firm feel to the floor. If your floor is solid, I personally don't see any big issue with running parallel to the joists. I'm equally sure you will get a lot of differing opinions. Good luck!