Where your foot is on the platform may or may not matter depending on the machine. What I am talking about is your hip, as far as how much it is abducted/adducted/rotated, and also the rotational position of your knee. Some people adducted their hip and rotate their knee in, as compared to using two legs.
The other part that matters is the pressure on the knee, the smaller the angle behind the knee and in front of the ankle, the greater the force on the knee.
The rectus femoris is involved in knee extension and hip FLEXION. It's not involved much in hip extension, that's more glutes. All leg presses have varying degrees of hip extension, and this can be changed not only by machine, but also your position. If you notice, when you get more hip extension, you feel it a little in your hamstrings. Same thing with lunges, wider stance ( more hip movement) gives you more hamstring involvement.
It is the upper portion of the hip extension that is eliminated entirely in a vertical leg press. Your internal hip flexors in the lower abdomen are only used isometrically, the abs are just resisting internal pressure, and the lower back is do practically nothing.
I actually consider that to be a benefit of the machine. The disadvantages are the location of the plate posts, and positioning yourself on the machine.
Given your concerns about hip extension, when you use the hack squat, my guess is your leg is way far back, and you go too low as well. That will definitely give you knee pain.