This functionality is actually already possible on all elements with background images except on the browser fill. You can insert a background image, and then in the Fitting drop down, select either "Scale to Fill", or "Scale to Fit", whichever you are looking for. We are currently exploring our options in allowing this for browser background images, but in the meantime I would recommend making a post over on http://forums.adobe.com/community/muse/ideas. We keep an eye on ideas there and how many votes an idea has and use that to help us prioritize our features a little better.

The effect seen on that site would be acheived with a "Scale to Fill" background. They, however, do use some JavaScript on the page to get the effect with multiple different images, and it is done using an element that resizes to be the full browser size. This effect, with a single image, would be possible in Muse with the ability to set this fitting on the browser background. And, while we do keep track of ideas on the previous community board, moving them here also helps new users put in their votes for these features.

You are correct. I was specifically referring to the effect within rectangles as you demonstrated. It is not yet possible to do this on the browser background. As far as the screenshot, there are known issues surrounding that specific scenario that we are working on improving. But, the effect on the site will not be possible without browser background fill support for the property because a rectangle cannot be stretched height-wise to fill the browser (as this must be done with jQuery). Once again, I'd recommend putting an idea in the idea section so new users can vote on it.