After a couple of hours of hunting I discovered that for some reason my "Bundle Display Name" was blank.
This can be found by selecting the "top level App name" in Xcode's Project Navigator (the left pane with all the files) and then selecting "the app name under Targets" and then going to the Info tab.
I copied ${PRODUCT_NAME} from Bundle Name and pasted it under Bundle Display Name. I ran the app again and connected it to iTunes and now my app is the appropriate iTunes File Sharing list.
See a detailed answer here:
How to enable file sharing for my app?