Publicly available doesn't mean you have a license to do whatever you like with the image. If I download an image and re-upload it to my own art station or sell prints of it, that is something I can physically do because the image is public, but I'm absolutely violating copyright.
That's not an unautharized copy, it's unauthorized distribution. By the same metric me seeing the image and copying it by hand is also unauthorized copy (or reproduction is you will)
Then I don't really understand your original reply. Simply copying a publicly available image doesn't infringe anything (unless it was supposed to be private/secret). Doing stuff with that image in private still doesn't constitute infringement. Distribution does, but that wasn't the topic at hand
The answer is "it depends". Distribution is not a hard requirement for copyright violation. It can significantly impact monetary judgements.
That said, there is also an inherent right to copy material that is published online in certain circumstances. Indeed, the physical act of displaying an image in a browser involves making copies of that image in cache, memory, etc.