While it has to be more permissive than 755, I stand corrected.

$ cp /bin/ls /tmp/ikegami/
$ chmod 777 /tmp/ikegami/
$ chmod 700 /tmp/ikegami/ls
$ perl -T -e'%ENV=(PATH=>"/tmp/ikegami/"); system("ls") and die("error
+: $?");'
Insecure directory in $ENV{PATH} while running with -T switch at -e li
+ne 1.
[download]

(I used /tmp since I don't have root access.)