A work around would be to have the first address in the list be one you don't mind showing up in the headers. As for what is causing this problem... I'm sorry but I don't know. I usually do something like:

open(MAIL, "|/usr/lib/sendmail -oi -t") || die "Can't open sendmail: $
+!";
print MAIL <<MESSAGE;
To: $email
Bcc: $bcc1, $bcc2
Subject: $subject

This is an automagically generated message, please do NOT reply to it.

MESSAGE

print MAIL "More text goes here";
close(MAIL);
[download]

EDIT: you could use a foreach loop to add enough Bcc: addresses.