Why can't I get the output of a command with system()?

You're confusing the purpose of system() and backticks (``). system() runs a command and returns exit status information (as a 16 bit value: the low 7 bits are the signal the process died from, if any, and the high 8 bits are the actual exit value). Backticks (``) run a command and return what it sent to STDOUT.

    $exit_status   = system("mail-users");
    $output_string = `ls`;