You actually see this quite a bit. It's called "feel v. real". There are videos of A-Rod doing the same thing. Here's a video of Matt Antonelli explaining it, using A-Rod's swing.
I don't actually believe there's anything wrong with teaching "feel v. real" and in fact, I actually use this with some of the 8 year olds I coach. They naturally have large uppercut swings, which don't work well. So before every game, when we do side toss, I tell them to hit the ball off the base of the net and those kids will take some really awkward choppy swings to hit the base of the net. But - we go into game situations, that "feel" has really helped them level off their swings and both of them are performing much better since we made that change.
An issue I see is that coaches/instructors should know "feel v. real" and they should know that when they are preaching that old school, hit down on the ball approach - that it's actually just a mentality or feel and that you'd actually never swing like that in a game. That should be explained to people. I'm not so sure A-Rod or Miggy (or Donnie Baseball???) know that.