Some websites are only accessible when you're logged in on that site. That means that even if another person goes to the same URL as you, he or she will see different content or won't be able to access it at all.
So you can't heart images from private pages, because other users won't be able to visit the site that they came from. But on many of those sites, you can get a link to the original content (permalink) that is open to anyone.
Google Reader displays posts from the RSS of blogs you subscribe to. You need to be logged in to access this page and it's different for every user, since people may subscribe to different RSS feeds. Here's how to go to the post permalink and heart the image from there:
Click the post title and you'll go to the posting page (permalink). Then use the bookmarklet on that page.