Mehdi gives an answer to this question in the Stronglifts Report. It is not based on actual science, but rather anecdotal evidence, I quote it here. (Page 58)
Watch out by the way with people telling you to do half Squats instead of hitting parallel.
Half Squats are NOT safer for your knees, they can actually destroy them because they
cause muscle imbalances (lots of quads development, but little hams/glutes). Your body is
designed to Squat below parallel. Why do you think babies naturally sit in the bottom
Squat position when playing with toys? And if this was really bad for your knees, wouldn't
your body be designed in a way to prevent you to Squat parallel in the first place? Indeed.
The whole “Deep Squats Are Bad”- myth is spread by gym bros who hurt their knees by
doing Squats wrong, which is how the large majority of gym goers do it. I challenge you to
find 10 guys in your gym who Squat with proper technique. When these guys now go get
help for their painful knees, those dumb doctors wrongly conclude that the exercise was
the cause instead of the bad technique. I've only met one doctor so far who recommended
me to Squat parallel. Frankly, I was stunned. But then again, he did Squats. All other
doctors, past and present, told me that lifting weights is bad for your health, even though
the American College of Sports Medicine – the largest sport medicine & exercise science
organization in the world – recommends weight lifting.
I talked to a sports medicine doctor and he agreed on this. As long as it isn't painful and you watch for correct technique, deep squats are safe. This means, focus on correct technique instead of increasing weight. If things get too heavy you are likely to adapt a bad technique that brings your knees in trouble.
Another thing is that your joints and bones are not growing as fast as your muscles. If you just started out with doing sports you might want to take it a bit slower as they need some more time to adapt to the new circumstances.
There is also a video Medhi made where he explains (and draws) how to properly deep squat.