Matt, I think in the above scenario, the guidelines are going to disagree with you. Why? Well, the guidelines do state that if the image requires a text equivalent, which this one does, the alt attribute needs to be populated with the appropriate text. Leaving it blank goes against the guidelines. Also, that image, when processed by someone using assistive technologies, may help them to solidify the page. I'm going to assume that the surrounding text is discussing a vacation to Mount Rushmoor. Describing the picture to those listening is good practice and is suggested.
There are definitely decorative and functional images. For example, a decorative image might be a round bullet used adjacent to a link. Not a best practice, but a good example of where an empty alt attribute would be required.