A family member's MacBook Pro seems to have the "Secondary Tap" action mapped to program switching instead of popping up the context menu. This happens when a mouse is plugged in as well as when two-finger tapping the trackpad.
No preferences related to what the right mouse button should do come up when looking at the mouse preferences.
Googling so far makes it look like a Magic and/or Mighty Mouse could have caused some of these weird issues if it was plugged in at some point but we don't have one available now. I have not been able to figure out if these prefs actually exists on the machine and, if they do exists, how to remove them.