I think winter and summer are mixed up in the picture on this page. The Moon follows the Sun's path and the Sun certainly does not rise high in the winter and low in the summer.
Here's a copy of the image from the page you mentioned:
Credit: Goddard Space Flight Center
The Moon's path (and thus appearance in the sky) will depend on the season.
The figure is correct the way it is drawn. To understand this, imagine the geometry of the Sun, Earth and Moon during the full Moon phase; the Sun and Moon are on opposite sides of the Earth. In the summer the tilt of the Earth's axis has us pointing toward the Sun during the day, so at night we must then be tilted away from the Moon. Because we are tilted away from Moon, it is lower in the sky. In the winter the situation is reversed and we are tilted toward the Moon at night and away from the Sun during the day.
Laura Spitler was a graduate student working with Prof. Jim Cordes. After graduating in 2013, she went on to a postdoctoral fellowship at the Max Planck Institute in Bonn, Germany. She works on a range of projects involving the time variability of radio sources, including pulsars, binary white dwarfs and ETI. In particular she is interested in building digital instruments and developing signal processing techniques that allow one to more easily identify and classify transient sources.