Works:
    SELECT * FROM link_users_access
    ,access, link_guilds_access
    WHERE access.id=link_users_access.access_id
      AND access.default_level < 10000
      AND link_guilds_access.access_id=access.id
      AND link_guilds_access.access_level < 10000
      AND link_users_access.users_id=1
      AND link_users_access.guilds_id=26

Does NOT work:

    DELETE FROM link_users_access
    USING access, link_guilds_access
    WHERE access.id=link_users_access.access_id
      AND access.default_level < 10000
      AND link_guilds_access.access_id=access.id
      AND link_guilds_access.access_level < 10000
      AND link_users_access.users_id=1
      AND link_users_access.guilds_id=26