How do I update the information in a site collection's "user information list"?

So, I am looking into why a site collection's user information list does not reflect the User Profile Service Application (UPSA)'s data.

A user moved from department A to department B. Their Active Directory entry changed last night.

When I go into SharePoint's UPSA configuration screen, go to manage user profile, and search for the user, his account and department have changed.

When I go to the site collection's user information list, it shows the updated account - but not the updated department and user name.

I check the appropriate timer job - it is running every hour with a success. I even force a run of the timer job. It finishes in a minute, reports success - and yet the user information list still reports stale department and user name information.

I ran set-spuser $user -SyncFromAD and did not get an error.

I have looked at the portions of AD to which I have permissions to read. The user's AD information has been updated to department B.

When I go to the user information list, and look up the user, his department is department A instead of department B as it should be.

If set-spuser does not work, then is there anything that will?