I'm unclear about what is being asked here.
If I set up my camera and then ask someone else to take the shot, I am not going to claim I took the picture.
If I set up my camera and then ask someone else to take the shot, I do believe I own the picture. (owner but not photographer)
Even though I own the picture, if the picture had some financial value, I would be hesitant to cash in on that value without sharing it with the person who took the picture, as they could very well have a legal right to a share of the profits. People sue one another all the time to get a piece of anything they were remotely connected with and it's almost always cheaper to work that out beforehand, rather than in court.
For me, personally, pictures triggered by infrared or other automatic remote triggers are a bit more grey. I guess it would depend on how much involvement I had in setting up the shot and how much was just chance. I'd certainly own the picture in any event, but how much credit I would take for it would depend on the circumstances.
No clear legal answers because each circumstance would have to be litigated. Which is something I can usually avoid since my pictures have more personal value than financial value.
If you really want to spur some controversy, try getting your head wrapped around these "appropriation artists"
Sherie Levine http://www.metmuseum.org/toah/works-of-art/1995.266.2
Richard Prince http://www.richardprince.com/photographs/cowboys/