Simple solution - don't use tabs in browsers.
I don't think this solution fixes anything. As near as I can figger, the guy that uses multiple windows (instead of tabs) is just as vulnerable to this issue as the tab user --- assuming that his top window(s) block the view of other browser windows entirely. The only real issue I see in the article is that, when your attention is diverted from a page and it is hidden from your view, its contents may be changed.
So, tabs are, as far as I can, a red herring here. It's not really about tabs at all. (Someone may correct me if I've missed something.)
The first thing I do to any browser I sit in front of, is to immediately disable the use of tabs. I have never understood why many people think they are a good idea - I think they break a heap of good UI principles.
Thank goodness that your loyalty to UI principles does not restrict my browser's features. I don't want a dozen browser windows, taking up space on the screen and making it difficult to find what I want. I want one window with tabs that have visible icons and (partially visible) titles, so that I can pick the right tab quickly.
Maybe it is an inconsistent use of the ideas of tabs, but it's damned useful nonetheless.
In any case, your primary criticism about tabs has nothing to do with this security issue.