If one wants to include an image in a post here you have two options. You can use the inline format:
Or you can click the "Image" icon in the toolbar, and paste the link there. This latter method will result in the image being uploaded to imgur and the link to that site included in the post, while the former method will result in a hotlink to the original site.
From these two questions it seems like hotlinking is generally safe from a copyright perspective. I would assume that uploading an image to a third party site would very much not be safe, as it is clearly causing a copy to be made.
The example that prompted this question was this post, where the results of two papers are discussed with reference to the figures from the paper. I would have thought that with hotlinking it is used exactly in line with the aims of the site, to stimulate discussion of the issues raised in the paper with reference to the results. I would not expect anything to happen in this case, but academic publishers have been quite defensive about their intellectual property and I would expect them to have a case if they complained about the reupload of the images to imgur.
What are the legal considerations here? Should we all be avoiding the "Image" icon in the toolbar unless we have the right to make copies of any included images? Is there a copyright exception that allows reupload of images available on the web? Is there something else that make this OK? Or is even hotlinking copyright breach and so no images should be included unless we have the right to make copies?