I'd consdier this pilot error, or at worst a doc bug.  I see no reason
why syslogd *should* write /var/run/syslogd.pid when "-u"ed to some
random user.

If it's being done for least-privilege use for the main syslogd for a
host, then the simple thing is to chown the pidfile to that user when
you chown the logfiles to that user.  syslogd won't be able to remove
it on exit, but that won't bother it, and it'll get rewritten on next
start.

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