Seems like App Inventor is too 'BETA' at this point. No help *anywhere* on how to get around the problem of uploading media files along with your application to the phone.
It is a workaround and painfully manual, but this worked for me at least with myTouch phone:
1. Once your app is ready, hit 'Package for Phone' dropdown and 'Download to this Computer'.
2. App Inventor creates a local .apk file. Connect your phone using USB cable.
3. Copy the APK file to the root of the "Removable Disk" (the phone). **Disconnect the phone**
4. Using Android Market, search for "Apps Installer" and choose a better rated one.
5. Once you install the Apps Installer, run it.
6. The installer finds your App and walks you through the installation process.