Turns out the following code doesn't set the image content of an ImageView:
Uri myImageUri = Uri.parse(myImageAddress);
If you inspect the LogCat log, you'll see a message something like "resolveUri failed on bad bitmap uri". Here's what you need to do instead...
URL myUrl = new URL(myImageAddress);
InputStream inputStream = (InputStream)myUrl.getContent();
Drawable drawable = Drawable.createFromStream(inputStream, null);
That should work once you've wrapped the necessary try/catch statements around it and set the "internet" uses-permission in the AndroidManifest file of course.