Example 1.
Using public file system, enter the URL of an image in the Web tab of the media popup.
Works as expected.

Example 2.
Install and configure the amazon s3 module as the default file system.
Enter the URL of a remote image in the web tab of the media popup.

Instead of the expected behaviour, this error is displayed instead:
The specified file temporary://foobar.jpg could not be copied, because the destination directory is not properly configured. This may be caused by a problem with file or directory permissions. More information is available in the system log.

If using the upload tab (instead of the web tab), the file is sent to S3 as expected.