Of course you can.
Birds can fly too. 
There is a higher chance of your knees getting injured if your
knees goes beyond the toes. Most people know that.
If your knee hurts when full squatting, you're probably going
into a knee dominant squat rather than a hip dominant
squat(which is what you should be doing). Initiate the
movement downwards by pushing your hips back, not by
bending your knees. Imagine sitting back into an
imaginary chair, not sitting down. You might benefit from
some box squats to practise your form.
Its amazing how you can disagree for the sake of
disagreeing.
I think the bolded description(quoted from your words) is clearly
demonstrated in the picture.
What i am confused is how you can call that not a squat.
