Yes the teasing thing is a myth. I know of plenty of mares who while bred, will show and even allow a stallion or gelding to breed them.
Mares also have regular cycles and presenting them to a stallion between cycles will not make them magically ready to breed unless they are a hussy that will stand for breeding at any time (know mares like this too
). Being near a stallion does not cause a mare to come into heat. Her natural cycles do.