I think that I can answer that one. The problem that tellywellies is referring to is when people post a link to someone else's site in order to show an image by their name - like your little man. If your little man was on a site of graphics and you linked direct to that site instead of copying the image to your own webspace, then we would have a problem.
Some websites invite you to use their gifs but they do not want you to use their bandwidth, they have to pay for it. It might sound as if the money is insignificant but multiply that by thousands of people and it mounts up.
It is also necessary to check that the image is not subject to copyright, I know that one site I checked on more or less said that it was using the images on its site without permission, it asked not to be sued!
In the past FT has received complaints about images being pirated, it is not fair on the owner of the site to have to apologise for what the members of this site have done.
Silverginger made an offer to members of FT, he said that he has ample webspace and was willing to host avatars for members so there is no reason for members to link direct to sites when they shouldn't.
You can certainly post a clickable link, that is not a problem unless it is only to an image, then sometimes the host of the image will block the link - Tripod springs to mind. Most sites are happy for you to link to their pages, it gives them more traffic.
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Many a child has been spoiled because you can't spank a Grandma!