This is why I referred to the different muscle involvement. If I'm training someone's muscle memory, it doesn't help them if I let them practice improper intent, as that usually involves different muscles (or at least different usage of the muscles) than the desired intent. Now, it's not actually necessary that they know the intent in order to do the right movements, but it's often easier to get them do use the right muscles if they are thinking of the right kind of force. There are some exercises that train the right movements and muscle involvements through a different intent, and those are just as useful. Here's the example I use: if I have a student who did Tae-bo for 10 years, I may have a hard time training them to good kicks, because they've learned a similar motion, but with all the wrong muscle involvement (many of the kicks in Tae-bo are too focused on speed and retraction, so no power in them, and no balance when hitting a target). On the other hand, if I have a student whose prior instructor had them standing for a few hours kicking in front of a mirror WITH PROPER INTENT AND FORM (correct muscles, proper balance for the strike, etc.), I can probably get them to kicking with some power fairly quickly.
Mind you, in some cases it may be easier to get someone to move right if they DON'T know the intent. We've all had students (or worked with them) whose "natural" movements were unusual, and who had to learn an entirely new habit in order to do some of the "easy" techniques. I have a student right now who has trouble with rolls. I have him (an adult) imitating an orangutan (including the noises), and his rolls are much better.