I removed the "upload" handler from the damSupport, so that the Editor can only choose an image from DMS.
This is what I've done:
Templating Kit --> Site Definitions --> <my site> --> damSupport --> handlers --> upload.
I set the "enabled" property of this content node to "false".
This way, the Editor can only choose an image from DMS (she can not upload it directly).

If the DAM support is configured like this, with only one handler, the information about the image is not saved correctly.
For example:
If the name of the property that stores the image is "myImage", then when there are two handlers, after saving the image, in JCR browser I can see that there are two nodes for the image:
1. myImage = dms
2. myImageDmsUUID = 766a6d0d-4f96-45d8-a6a6-575bace65636
But with only one handler in place, all I get after saving the dialog is:
1. myImageDmsUUID = 766a6d0d-4f96-45d8-a6a6-575bace65636

Now when I test for the existence of the "myImage" property in freemarker, I get result that there is no image.