It's not about "Keeping Heels Down", it's about "Allowing Bodies Weight To Flow Naturally Into Your Heels"...
I'm not a trainer, but a trainee...but sometimes it helps to hear the student side:
I started riding at 50, and many of my problems have been from very tight legs and hips. It is nice to hear "Heels down", but not much use if your legs won't allow it to happen without conscious effort. And if I did the latter, then I was riding with heels down AND with tension in my leg - so I bounced and was unstable.
When a person starts riding, his legs & hips may not allow the 'proper' riding position. I would have the student sit on a calm horse, and preferably several horses - a wide horse will cause a different position than a slender horse. At a standstill, check to see what will allow the student to have the best position without tensing the leg.
For example, as you move your leg forward into a chair position (evil, I know), the toe can go forward and the heel can go down without tension. But by the time my heel is under my hip, it will be level at best - and that is after 3 years of riding several times a week.
On a wider horse, my toes drift out because that is the only way I can get my legs apart to be on the horse. And if that means my cues are not given optimally...so be it.
As you experiment with different leg positions, explain to the student the impact of moving the leg. Ideally, the stirrup leather should be straight down when the student's bum is in the deepest part of the saddle - so show the student what happens when you use too too big or too small a saddle for the student's body. Let them see how a wide horse vs thin horse affects their leg, and how moving their foot forward or back impacts their heel and calf.
Then you can explain both the goal to strive for, and also what the student must do NOW to have the most secure seat he is capable of having. In my short experience, a secure seat requires a loose leg. The more tension in my leg, the less secure my seat - so I accept, for now, an imperfect position to get a relaxed leg.
With time, my heels are drifting back and my toes are drifting forward, but that is a trend. There is a wide horse where I take lessons. He is probably twice the width of my Arabians. It is like sitting on a dining room table. When I ride him, my legs move forward and my toes move out because that is the only way I can relax into the saddle. OTOH, using an Australian saddle on my 825 lb gelding, my heels are under my hip now, and my toes mostly forward, while still having a relaxed leg.
Just making a plea to understand where the student is at. I've had several people tell me things based off of what THEY can do, or off of what the GOAL is, without any regard for the limits my body imposes NOW. Believe me, a 53 year old male doesn't have the flexibility of a 14 year old girl!