I don't know if it's true or not, but a friend who's trying to get his kid into Harvard told me there is no tuition, assuming you can't afford to pay. Sorry for being able to offer only an anecdotal comment.
Don't you think if anything like this ever became law, (which is far removed from where we are now) schools with huge endowments would not be included or would cover the cost for students without money who get accepted, like they already do?