No. A link alone is OK. Even an inline-linked image or video is OK, and the previous board software just showed the image you linked to without downloading it to SB's server. Other forums like e.g. Wetpixel still just show linked images from their original location. Go to one of the image threads, like
this one, right-click on the image and check its address. It's not hosted on Wetpixel, it's hosted where the owner put it.
But if you paste that link into the image function here on SB with the current board software, either you, SB, or both (I really don't know whose responsibility it really is) are breaching copyright because of what happens in the background here. Do the same right-click thing on an image in a thread here on SB, and you'll find that the image is hosted here. Because, as I said, the board software downloads the image and displays the downloaded copy.
If it's your own image, you aren't doing anything wrong, because you as the copyright owner are uploading the file to SB's server, which grants SB the right to show the image. Even if you don't know that you're doing just that.