Our horses also realize we are in charge. Because we give them a choice, and when they make the wrong choice, there are consequences. They are rewarded (by taking off pressure) for making a right choice.
Sorry, but this is rubbish.
A choice is only truly a choice when ANY answer can be correct and followed through. By not accepting the wrong answer, no matter wether you do it by making the right thing easier, or by only allowing one reaction, you are NOT giving your horse a choice.
A choice would be - Do you want to be ridden today? And if the horse chose no, you turned around and left.
'Giving your horse a choice' is baloney. You may think you're giving them a choice, but if you can handle your horse safely and ride it, then it didn't have any choice. No horse chooses to let a predator on their back, no horse chooses to be confined by a halter or a stall, no horse chooses to surrender it's freedom by picking up a foot.