Looks like a real bug in Sys::Syslog. Below the code from Syslog.pm around line 632:

        if ($_ eq 'kern' || $num <= 0) {
            croak "syslog: invalid level/facility: $_"
        }
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Changing this to

        if ($_ eq 'kern' || $num < 0) {
            croak "syslog: invalid level/facility: $_"
        }
[download]

makes the code work for me.

Update:Of course that change means you won't get an error message anymore if you forget to specify a priority (e.g. syslog(LOG_USER,"test")). I'm sure someone will come up with the right solution though.