>If a digital artist creates a painting and puts it up on their website, and you go view it, it does not become yours.

Of course the image is mine, just as an image of the painting in a newspaper or brochure would be mine, it's a copy freely distributed by the copyright owner. I'm perfectly within my legal rights to do whatever I want with it, within the confines of the browser.

I'm not claiming i have the right to sell it or anything, but I absolutely do have the right to decide whether or not it shows up.