No I don't think i misunderstood anything. If any instructor doesn't say 'inside of foot' what they will say is 'load on the ball of the foot'. Never have i seen 'on the heel'.
If loading was supposed to be done on the heel then we would see that every day on this site. People would be writing on advice seeking threads: "You're not loading your weight on your heel. Load your weight on your heel and then transfer it to your toes." I'll bet that has never been said on this site even once.
In any sport when there is a heel to toe transfer the athlete continues to throw the whole body in the direction of the toe. Look at any olympic long jumper, high jumper, runner, a running forehand, an outfielder making a running throw to home plate, a javelin thrower, an american football player, frisbee throwing, basketball, etc. All of those sports have toe to heel transfers and with every one of them the player continues to move the whole body in the direction of the transfer which is in the direction of the toes. Tennis players plant the foot pointing to the side fence then transfer weight to forward into the court which is perpendicular 90 degrees off of the direction of the toes. so there is no heel to toe transfer.
Safin has excellent technique. Look at this vid. clear slo mo. look at his right foot. He's clearly not loading on his heel. Most of the time his lifts his heel and his foot actually slides backwards behind his body. No heel loading or heel -> toe weight transfer