I believe if you have custom fields that you created for either people or companies that are important and or specific to your business tracking, you should be able to select those as a key field for importing.
We have a 1600+ people database that we also manage inside of a CVS spreadsheet. Although the first import went well, our second update that we wanted to import(that had multiple updates) won't work because of the minimal key fields to select from.
Yes, we should have done more research and done an export after our initial import to also export a list to work off that list, but we didn't know.
Allow custom fields to be key fields for imports while trying to "Identify matching records by:".