How can someone with ptsd "grow out" of it without treatment?

Benefit of Time. This will vary depending on the person and his/her expereinces, but it is possible for symptoms of ptsd to lessen over a period of time. A lot of this has to do with no further traumatic experinces and exposure to a nurturing, supportive environment. So, in a sense, there is still a type of treatment - it may just be environmental and supportive instead of formal mental health treatment.
Safety. I agree with dr. Holmes. Ptsd symptoms may abate over time when the environment is perceived as safe and there is no further threat to the person. This is more likely to occur with simple ptsd or mild ptsd.