What version of InDesign? (Look at InDesign CC menu > About InDesign on Mac, or Help menu > About InDesign in Windows)
What operating system?
There's CC, CC 2014, and CC 2015. Will you show your About InDesign screen to display the exact version?
In the meantime, the best way to transfer files is for the InDesign user to package them with File > Package, zip it and sent it to you. Not only will you receive the InDesign file, fonts and assets, you will receive an .idml file that can be opened on CS4 or later.
El Capitan 10.11.6
InDesign CC 9.3 - When I go to Updates, it tells me I have the most recent version.
That's CC. The current version is CC 2015.4: 220.127.116.11.
If you have a subscription—and you must to be on CC—it's a free upgrade.
Your version is very old.
With Creative Cloud version of InDesign, you need to get updates from the Creative Cloud desktop app (on the menu bar on Mac, task bar in Windows). It sounds like you're looking at the Updates command in the Help menu of InDesign.
This document explains how to work with the CC desktop app:
Before you do it though... a quick heads up on upgrading to the newer versions. The desktop app deletes the old ones automatically when you install a new one. If you want to keep your version of CC for any reason, read this before you download and install CC 2015: