mysqldump: Got error: 1: Can't create/write to file 'dumpdir/tablename.txt' (Errcode: 13) when executing 'SELECT INTO OUTFILE'

[Mike Spreitzer]

So I am trying to use mysqldump --tab for the first time.  I am running 
into the same problem everybody does on their first try --- Errcode: 13. I 
have set the permissions on the target directory to be completely liberal 
--- anybody can do anything with it --- and I still get Errcode: 13.  I 
can even write into that directory when logged in as mysql (UID 100, GID 
100, and yes that is what the mysqld process is running as).  What's going 
wrong here?

[root@xd026 ~]# cd /
[root@xd026 /]# ls -ld dump1
drwxrwxrwx  2 mysql mysql 4096 Feb 22 18:31 dump1
[root@xd026 /]# ls -l dump1
total 8
-rw-r--r--  1 root root 742 Feb 22 18:31 red1_p2.sql
[root@xd026 /]# su - mysql
-bash-3.00$ cd /dump1
-bash-3.00$ date > foo.bar
-bash-3.00$ ls -l
total 16
-rw-r--r--  1 mysql mysql  29 Feb 22 18:38 foo.bar
-rw-r--r--  1 root  root  742 Feb 22 18:31 red1_p2.sql
-bash-3.00$ 

Thanks,
Mike