ok...I will admit there is difference between a bully and an alpha horse after thinking about some of the things I seen. Now that I think about it, I have seen a horse run another up and down the pasture for no reason that were not the alphas HOWEVER...I do still disagree that the alpha is a "passive" horse. Maybe that's not the word you are looking for, I don't know but passive would not stay alpha long. I still stand by my original statement that the alpha DOES need to be KIND OF a bully. Passive, nope. Maybe level-headed is a better word but passive is going to get the herd in trouble or he/she is going to be lunch. Passive is non-aggressive/inactive; receptive to outside impressions or influences which is NOT by definition an alpha. Those two words contradict themselves.
Also, I don't take everything Mark Rashid, since you want to site him so much, says as gospel as you all like to say ..take from everyone and learn all you can.