It looks like the issue can be reduced to whether or not to show this
output:

  >>> import os
  >>> os.write(1, b'should we see this in idle?\n')
  should we see this in idle?
  28

assuming sys.__stdout__.fileno() == fileno(stdout) == 1.

If "should we see this in idle?" is shown in idle then the output that
writes to the inherited C stdout such as os.system('ls'), 
subprocess.call('ls') will also be shown automatically.

And in reverse If "should we see this in idle?" should not be shown 
then other C stdout output such as produced by os.system('ls') should 
not be redirected too. The output written to the same file should be
shown/not shown consistently.

  os.write(2, b'the same goes for stderr\n')