Is a horse untrainable for Riding

I had the best discussion with some one over the last few days about if a horse can never be trained to be ridden. It all started with this one individual who was asking about her mare that she was getting saddle broke. she was having a hard time getting the horse to accept her being on, and so she got rid of it. When I heard that I was like whoa that's not the horses fault. So I replied and said that theres no such thing as a horse that is untrainable. Then I got the response of well now how many horses have your trained. I replied its not how many horses I have trained, it's the results that I get with that one horse. Then it went on again saying that they have taken that horse to some very professional trainers and even they couldn't get the horse to be trainable.
Ok first let me tell you that horses are doing what they need to do to survive. Survival comes first before anything else and this is way horses have leaders in a herd. If they didn't have one then there wouldn't be any issues cause the horse isn't afraid of anything. So by understanding horses behavior and such we can prove to them that us humans are even better than their horsey leader.
Second, its the humans fault that the horse is behaving this way. Horses don't say oh I'm going to make this tough and what not, they learn by how you act and teach them.
Third, what good is it to take the horse somewhere else to have it trained? I do agree that there are many great trainers out there, but not very many good horsemen. I like to use the example of a baby sitter. So your parents go out and have a baby sitter come to take care of your kid while your gone. So theres to kinds of baby sitters, well three. One is the one that doesn't care what you do and what not. Two, some one whose telling them what to do all the time like homework and bed times and such. Then you've got the one that's in the middle. suggesting that you should do homework, but if you want to play that's fine. So depending on what kind of a person you give your horse to will either have a great time with you and want to see you every time, or your horse will hate them and make things worse. I mean have you noticed that horses tend to go to other people besides their own owners. Your horse is showing you alot when going to other people for compfort it means that your not showing your horse that he can rest and be safe with you and seeking comfort with other people because he knows that there not going to make him work.
So by having your horse sent off and then coming back to you, your only teaching the horse that you really have no clue what to do with him and so hes never going to change for you. So why not build a relationship where you and your horse want to be together and him not looking for options out and getting substitutions.