結論：svn/dav, svn/dbの権限変更が必要

下記の二つのDIRにapacheを動かしているユーザにオーナー権限を与えます
/usr/local/svn/dav #activity databaseというものらしい
/usr/local/svn/db #transactionログなどか

   1  # chown www-data:www-data -R /usr/local/svn/db
   2  # chown www-data:www-data -R /usr/local/svn/dav

エラーの内容など

   1  $svn ci -m "test"  
   2  svn: Commit failed (details follow):  
   3  svn: Can't create directory   '/usr/local/svn/db/transactions/1128-1.txn': Permission denied  

→ chown www-data:www-data -R /usr/local/svn/db

   1  $svn ci -m "test"
   2  svn: Commit failed (details follow):
   3  svn: Can't open activity db: APR does not understand this error code

→ chown www-data:www-data -R /usr/local/svn/dav

Refs

http://svn.haxx.se/users/archive-2005-10/0084.shtml
http://svn.haxx.se/users/archive-2004-02/1350.shtml