As a Pushpage2010 Manager:
  1. Navigate to onMessage > Communication > Pushpage > Pushpage Templates.
  2. To the right of your Template with the rebellious images, click Edit
  3. In the regions that contain images, click Edit.
  4. Click the HTML button in the upper left corner to view the HTML, and remove the domain part of the image URL.

For example, the URL should go from this

to this:
User-added image
5. Click Apply Changes in the region.
6. Click Save & Exit on your Pushpage Template.
7. Navigate back to the Create Issue link, and create an Issue from the template to verify that the image is displaying.