Update: Sigh, I am indeed wrong as ikegami points out below. Error number 13 is "Permission denied" under Windows.

That's not what I said. I said system returning 13 means the child died from SIGPIPE. It does not mean Permission denied on any OS.

Now, if system returned -1, then you'd check $!, and if $! then contained 13, that would mean that system failed because of a permission error (on Windows and linux). But system did not return -1, which means the child was executed successfully. Neither system nor ls reported a permission errors.