I had a similar problem with a Makefile a long time ago. Make used whatever shell was in the user's environment rather than defaulting to a /bin/sh-like shell, and everybody used /bin/csh at the site. So I had to explicitly set $SHELL to /bin/sh in the Makefile.

Extrapolating to Perl, have you tried explicitly setting $ENV{'SHELL'}=/bin/sh before running your backticks?