Syslog not logging

You could also do the following which will make it so they don't go in any other logs:

local0.*                        -/var/log/haproxy.log
& ~

The & ~ means not to put what matched in the above line anywhere else for the rest of the rules.

It looks to me like you have a typo in your postgresql.conf file. Make sure that you're actually using

syslog_facility = 'local0'

Also, old syslogd required that hard tabs be used instead of spaces in your config file, so make sure that you aren't actually using spaces, or that your editor isn't converting tabs into spaces (such as the expandtab option in vim).

You also mention both old syslogd and rsyslog, so check to see which one you are actually using. Rsyslog's config file was designed to be backward compatible with syslogd, but does use a different file. So if you are using rsylog then add your logging line to /etc/rsyslog.conf instead.

In order to prevent those messages from also showing up in /var/log/messages you'll need to explicitly filter out that facility. In order to do that, modify your config for messages to this:

*.=info;*.=notice;*.=warn;\
    auth,authpriv.none;\
    cron,daemon.none;\
    mail,news.none;\
    local0.none          -/var/log/messages

That translates to, "Do not write any severity levels from the local0 facility to this file." Or, in effect, exclude anything local0.*.