db_query() doesn't seem to run in module
You write that


  but also make some changes to a record in another mySQL database that's connected to one of our internal non-Drupal systems


so I figure that you need to query a different MySQL database, but in your don't change the active database using db_set_active. This is most likely the root to your problem.

If the SELECT query works, then the code you have provided should work just fine.

A simple way to test your problem, would be run db_query on a known record and see if you can alter it. Devel also offers query logging, which would allow you to log the actual UPDATE and alternatively try to run the raw query through a MySQL interface.

Another explanation could be that you have the ismi.new_people table in the Drupal db, so you in fact are updating the wrong table/database.

Another possible problem is database  permissions. Do your DB user have read only access?