You could turn on Private Browsing (Safari Menu). That will delete the downloaded file automagically. Be sure to read the warning before you decide to do it. I've never tried it, in fact, just found it a minute ago. Maybe it's possible to just turn it on for viewing the pics, then turn it off.
(If you're using Safari) I don't think it hurts to try. You can keep them and put them back.I didn't get the green plus bubble, but it did create an icon on my Desktop.
Have you attempted this while logged in under more than one user account?
I don't do it often, but it hasn't failed me. I just grab the little icon next to the URL and the text comes with it. I assume you do that as well. But, just for grins, try holding down the Option key, like when you want to copy something from one window to another. I wonder if there's a plist file that controls this which needs to be rebuilt. ???
No, er, thanks. But that was a highly intelligent way to end your post.
And, my post was not in response to one of yours (isn't this the first?) so why the grade school comeback? Note that I already indicated that it cuts both ways.
And your sources are? No one's an expert without attribution; or everyone is, on the internet.
Latin is still spoken at the Vatican, I suppose.