The problem is with an explanation like that, a myth is being perpetuated. It may have stopped him but for the wrong reason. The better, more appropriate response would have been the batter did nothing to interfere and F2 tried to make the batter interfere. Whether it stopped him or not is beside the point. The response would have been better supported by the rules if a protest is filed and the coach would know better if one of his batter's, while still in the box, gets called out for INT. At least, he would know his argument of "both feet in the box" is not a valid one even if he tried to pull it out of his a$.
Now, it is a headache waiting for another umpire.
Now you're talking about judgment, as in who initiated the contact, which, of course, is non-protestable. In this case, "both feet in the box" is a very important ingredient. If I were to use your response, which is also valid, that issue is now debatable, according to the defensive coach. Chances are pretty good that the result is a prolonged discussion as to who the offender is
Both feet in the box have nothing to do with anything..the box is not a safe heaven for the batter..