Index usage and update statistics do not correspond?
About: sys.dm_db_index_operational_stats

The data returned by sys.dm_db_index_operational_stats exists only as long as the metadata cache object that represents the heap or index is available. This data is neither persistent nor transactionally consistent. This means you cannot use these counters to determine whether an index has been used or not, or when the index was last used. For information about this, see sys.dm_db_index_usage_stats (Transact-SQL).
The values for each column are set to zero whenever the metadata for the heap or index is brought into the metadata cache and statistics are accumulated until the cache object is removed from the metadata cache. Therefore, an active heap or index will likely always have its metadata in the cache, and the cumulative counts may reflect activity since the instance of SQL Server was last started. The metadata for a less active heap or index will move in and out of the cache as it is used. As a result, it may or may not have values available.

See: sys.dm_db_index_operational_stats (Transact-SQL)
On the other hand, sys.dm_db_index_usage_stats, which is mentioned above, is only reset when the service is restarted:

The counters are initialized to empty whenever the SQL Server (MSSQLSERVER) service is started.