I'm going to skip over the likelihood of this parallel joist situation actually being true (I have a deep mis-trust of stud finders), and attempt to just answer your question.
Answer part 1 - can any of this floor (+ subfloor) come up without causing damage/serious inconvenience to you or the property? If so, then I would strongly suggest pulling up a couple of boards and having a look around. I (unfortunately) had to do this in an old bathroom because we needed to move a sink, and after tearing up some plywood subfloor and 3 floorboards found a half-disintegrated joist holding up one end of the room.
I don't think your situation will be the same (water damage less likely in a hallway), but if it isn't obvious where to screw in to stop the squeaking this should help you out.
Answer part 2 - you aren't likely to get much long-term improvement from just screwing through to the subloor. A long term fix will require knowing where those joists are (parallel or otherwise!)
In an older property of mine, we regularly encountered the situation where a joist would be located directly underneath an internal wall, making affixing the boards to them pretty difficult. If you can't find recognizable joists close to the walls - this could be why. We solved that one by sistering another joist to it to give us something to screw into.