How can I directly, wirelessly copy files between Galaxy S3 and Ubuntu?
There are multiple possibilities to do so. If the opposite direction is OK with you (i.e. initiating the transfer from your Ubuntu machine), you might want to take a look at apps like WebSharing or Samba Server, which require little permissions. AirDroid is quite famous, but you probably won't like its permission requests (with that app you can maintain almost all your device).

Initiating transfers from your Android device, some file managers might be interesting. So e.g. ES File Explorer File Manager (which I use myself). This app can even auto-discover your Samba resources, so you can directly copy files in both directions.

All mentioned solutions work via WiFi and require both ends (Android and Ubuntu) being members of the same network.