Is there a way to tell which file (script, specifically) executed a command?

There is no guaranteed generic way to do that apart from walking the process tree (by looking at the commands PPID, then that process's PPID, etc...).

There's a good utility for that though, if you're not trying to script something: pstree. It will give you a "graphical" view of the process hierarchy. Something like:

$ pstree -a
 ...
  ├─udevd --daemon
  │   ├─udevd --daemon
  │   └─udevd --daemon
  ├─urxvt
  │   └─bash
  │       └─pstree -ah
  └─xdm
      ├─X :0 vt7 -auth /var/lib/xdm/authdir/authfiles/A:0-g8w3zk
      └─xdm
          └─awesome
              ├─chrome
              │   ├─chrome
              │   └─21*[{chrome}]
              └─qmpdclient
                  └─{qmpdclient}

There are options to show the PIDs, show or hide the command lines, etc...