You forgot one thing

binlog-do-db=our_database  
binlog-ignore-db=mysql  
binlog-ignore-db=test  
replicate-do-db=our_database  
log-slave-updates

The option log-slave-updates takes SQL that was read from relay logs and records them in the Slave Binary Logs when the SQL is completed.

Please be very careful. You should never use binlog-do-db and binlog-ignore-db simultaneously. I wrote about this back on Jun 14, 2012 ( Configured MySQL replication but its not working ) which points to an old Percona article on binlog-do-db being dangerous.

SUGGESTION

Of the things you are using, you only need these lines

replicate-do-db=our_database  
log-slave-updates

You really don't need binlog-do-db=our_database once you have log-slave-updates working properly.

Unfortunately, you are not going to get those queries from mysql.slow_log. Why ?

There are two options evidently being used

• log_queries_not_using_indexes
• log_throttle_queries_not_using_indexes

According to MySQL Documentation (The Slow Query Log, Paragraph 9)

To include queries that do not use indexes for row lookups in the statements written to the slow query log, enable the log_queries_not_using_indexes system variable. When such queries are logged, the slow query log may grow quickly. It is possible to put a rate limit on these queries by setting the log_throttle_queries_not_using_indexes system variable. By default, this variable is 0, which means there is no limit. Positive values impose a per-minute limit on logging of queries that do not use indexes. The first such query opens a 60-second window within which the server logs queries up to the given limit, then suppresses additional queries. If there are suppressed queries when the window ends, the server logs a summary that indicates how many there were and the aggregate time spent in them. The next 60-second window begins when the server logs the next query that does not use indexes.

What this shows is that your log_throttle_queries_not_using_indexes is set so that SQL text is suppressed. You can verify this with

mysql> SELECT @@global.log_throttle_queries_not_using_indexes;

Since it is a global dynamic variable, you must login as root@localhost and run

mysql> SET GLOBAL log_throttle_queries_not_using_indexes = 0;

This should expose new queries entering mysql.slow_log, but you will never see what those previous slow queries were.

You must run this

mysql> SELECT @@global.log_output;

If you see FILE,TABLE that means there is a text version of the slow query log. You will have to get your SysAdmin to get you the desired slow log info (Starbucks GiftCard might be required for this one. If the slow log file contains the same messages, take your Starbucks GitftCard back.)