I didn't mean to imply that the passage was stating that her spaceship was moving slowly (even though the example posted is just two astronauts in space without ships, but that's really beside the point). I only posted the passage to serve as the source of my confusion: how dilated time results...
Here is a passage from Elegant Universe concerning two astronauts passing each other in spacesuits in space with some relative velocity:
“From George's perspective, he is stationary while Gracie with her flashing green light and large digital clock appears in the distance and then passes him in...
This is something I've wondered for a long time. In discussing time dilation in SR, you often hear something along the lines of, "If you looked into a spaceship traveling near the speed of light, you'd see the astronaut inside moving in slow motion, the hands on their watch ticking slowly..."...