- Given a feed that contains an URL or filepath - fetch that file into the CMS and register it as a file attachment field
- Given a feed that contains an URL or filepath - fetch that files text contents and save the content in a textfield
This is about processing the content data of a feed and resolving a reference (an URL) into content, not about fetching the feed source itself. Hence it's primarily a tamper process, and only a fetcher after that.
Feeds_tamper module is not a strict requirement unless you need to do rewriting on the fly. Out of the box, this module allows you to map to file fields, and will quietly download the file in the background without any further configuration.
Import a normal article RSS feed that supplies its images as enclosures
<link rel="enclosure" type="image/jpeg" href="https://farm6.staticflickr.com/5559/30102441272_3cf8a1f6de_b.jpg" />
and get the image to my local site, attached as a normal file, and rendered in my local teasers using image styles etc.
This happens immediately as soon as you start mapping an URL into a file field 'url' using the Feeds processor mapper.

OR
Import a media rss style feed :
<rss version="2.0" xmlns:media="http://search.yahoo.com/mrss/" xmlns:atom="http://www.w3.org/2005/Atom">
...
<item>
<title>RE.8 Rear cockpit diagram</title>
<link>http://thevintageaviator.co.nz/node/2800</link>
<media:content url="http://thevintageaviator.co.nz/files/images/re-8-gallery/screensize/re8-202-re-8-rear-cockpit-diagram.screensize.jpg"/>
</item>
And use Feeds to import each of create a https://drupal.org/project/media_gallery">Media Gallery local copy of all that data.