So, stupid question time: is there any good reason for not even allowing root
   to call TIOCGPGRP on any tty?  It's rather useless if you can only get the
   process group of your own controlling tty.

i don't have an answer, but, this seems somewhat related to 
the change from BSD getpgrp() to POSIX getpgrp() 4.4 gave
us ..  i've proposed that we have a getpgid() call that
is identical to the old getpgrp() (and also happens to be
compatible with svr4 :-).

if this is ever added, TIOCGPGRP could perhaps be changed also.