The Smith Squat as described in ExRx can be used as an alternative exercise to barbell squat. For novices, it can used to familiarize oneself with the squat movement, particularly with a trainer's assistance. For more advanced weight trainers, it can be implemented periodically after the squat has become stale (yielding less progress as when originally performed). I'm not aware of any scientific study suggesting Smith squats are not as safe as regular barbell squats.
Someone has argued that the path is unnatural and that the machine prevents the body from determining its groove. I assume, they feel linear or lever machines are not as effective or not as safe as free weights. Although this argument warrants consideration, I am not aware of any scientific or empirical evidence to support this claim. Free weights certainly offer more variety of exercises than machines, but why restrict yourself to just free weights, particularly since greater progress can be obtained from exercises you are not accustomed to. See Restimulating Progress by Changing Exercises.
Machines seem to be as safe as free weights; even physical therapists commonly use linear machines for rehabilitation. One closed-chain exercise used for knee rehabilitation is the Sled Lying Leg Press. Is someone suggesting physical therapists are doing more harm than good by locking the body into the machine's groove?
The Smith squat can be adapted to accommodate individuals that may feel pain on barbell squat. A center of gravity does not need to be maintained between the forefoot and heel since the machine can prevent you from falling over. Using a similar method we used earlier to examine the barbell squat, we can compare the torque forces of the Smith squat to the variations of the barbell squat.
Using the form recommended by the trainer mentioned in the original question, the knees do not travel as far forward and the depth of squat is restricted. Both factors result in less torque force in the knees and lower back. Regarding placing the feet slightly forward during the Smith squat, concern has been expressed there is additional stress on the knees as the feet wants to slide forward but doesn't because of the friction from the floor surface. I would argue, there is actually less stress on the knee and this stress is not necessarily unnatural. The foot and lower extremity endure far greater forces during running or jumping forward; the feet want to slide forward, but don't, because of the friction from the ground. You can calculate these vector forces using certain physics calculations. Many of our readers have probably calculated these forces in biomechanics, or kinesiology class.
You would be hard-pressed (pun intended) to find a leg press exercise that did not place the lower extremity in a force some consider 'unnatural'; the feet want to slide forward but don't, because of the friction. Again, analyze the Lunge or the Sled Lying Leg Press. Just try dowsing the bottom of your feet with Vaseline® (petroleum jelly), hop on your favorite leg press machine and see which way your feet slip. I must warn you though, make sure the leg press machine has a safety catch unless you want some hospital staff to have to remove it from the insides of your rear end.
Incidentally, if an attempt was made to lower the feet on the Sled Lying Leg Press, so they would not encounter the questioned stress the feet want to slide forward, but don't, because of the friction, the knee would endure far greater torque forces just as if the back were too vertical on the squat or smith squat. The rounding of the back is encountered when the limitations of hip flexibility are taxed on most any squat or leg press exercise. See Squat analysis. This can be controlled by the depth of the squat if hip flexibility is inadequate.
I do agree that a stance with the feet forward beyond what is necessary can be less than desirable. I recommend a form similar to that of the barbell squat: knees and hips moving forward and backward the same distance respectively, weight distributed between forefoot and heel. If modifications are made, perhaps to emphasize glutes or avoid pain in a bad knee, I recommend only subtle changes from standard form; move feet forward just a couple inches forward or minimum modification that will accommodate the intended goal.
Although greater relative intensities can be applied to specific muscles by emphasizing one muscle over another (auxiliary exercises), greater absolute intensities can be achieved when agonist muscles work together with similar intensities (basic exercises).
This freedom of movement during the Smith squat could also invite unexpected problems. During a Smith squat with feet under the bar, back can be inadvertently positioned much more vertically that what would be possible on a regular barbell squat. This is accompanied by the knees traveling much more forward than they are probably accustomed to. The heel can consequently raises from floor, adding to already exaggerated torque forces of knee. This is particularly true when there is inadequate flexibility of the ankle. This is the situation I believe you and others are referring to when you say Smith squats places more stress on the knee. This problem can be easily remedied using a similar technique as with the barbell squat.
The muscles and joint structures can adapt to most any stress. If any of the factors outline on the ExRx site are not adhered to, injury can result. See adaptation criteria. The potentially excessive freedom of motion during a Smith squat (discussed above) may result in inconsistent stresses to knee joint that make it difficult for adequate adaptation. This assessment may seem ironic given machines are typically viewed as more restrictive in motion.
Generally speaking, Smith squat is a safe exercise when guidelines are observed.