Copy/pasting images into CKEditor results in data URIs being embedded

There are two cases where the "Restrict images to this site" doesn't work properly:
1) If you copy/paste an image directly into CKEditor, it brilliantly converts it into base64 and the code is saved to the database, like so: <img alt="" src="data:image/png;base64, lots and lots of characters />
2) If your image is explicitly referenced using the full URL (I have got lots like this on my site as a result of using IMCE), like so: <img alt="" src="http://mysite.com/my-image-file.jpg" />
In both these cases, although the image is actually on my site it only gets displayed if I switch off the "Restrict images to this site" filter