Try first this:
# chgrp apache /etc/msmtprc
# chmod 640 /etc/msmtprc
msmtp will ask you to use 600 on user config file.
I ignore if it's required on system config too.
If it still complains try:
# chown apache /etc/msmtprc
# chmod 600 /etc/msmtprc
But if the message appears on httpd error_log
it could be the permissions of the msmtp executable the cause.
On Slackware sendmail uses the gid bit and a smmsp group:
-r-xr-sr-x 1 root smmsp 800040 Apr 24 2010 /usr/sbin/sendmail
Perhaps you should do a trick alike with msmpt executable.
Anyway the above are just workarounds to find the problem.
More late you should investigate the "secure" solution.