I have to say it's probably number 2.

[root@archaia /root]# su nobody
[nobody@archaia /root]$ perl -e 'open (MAIL, ">./foo");print MAIL "scr
+atchymonkey.\n"
;'
[nobody@archaia /root]$ exit
[root@archaia /root]# ls
bin  mod_perl_docs
[root@archaia /root]#
[download]

Note how there's no error at all, but the file isn't there.
Let's try it with -w :

[nobody@archaia /root]$ perl -we 'open (MAIL, ">./foo");print MAIL "sc
+ratchymonkey.\n
";'
print on closed filehandle main::MAIL at -e line 1.
[download]

Hmm, what's going on there?

[nobody@archaia /root]$ perl -we 'open (MAIL, ">./foo") || die "$!";pr
+int MAIL "scrat
chymonkey.\n";'
Permission denied at -e line 1.
[download]

What user does sendmail run as on your box?
Check the open() as above...