Interesting question, and I think it can be taken in several different ways as shown above.
I worked with a classical dressage trainer for a while, studying movement, self carriage, and lameness. She was always a firm believer that the western saddle itself was not a beneficial thing to the horse due to its limitations on the back. However, one day I had her check on my 2 yr old Blue Valentine filly. Almost immediately, she said "you are going to have to get this baby on some cows." It was my original plan for the filly anyway. It is true, at 4 yrs old now, that baby will do anything I ask her, but she absolutely loves cows. She will do what I ask, but there is definitely one thing she will pour her heart into more than another.
I am the type that always wants to prove someone wrong when they say it can't be done. Most of the horses in my barn came with labels of what they won't do, and they will all do any of it and more now. One mare was at a professional dressage barn where they said she would never be rideable and definitely never be safe around kids. Last season, she was winning open classes with a 12 yr old girl on her back against adults. The girl wanted to learn to jump, and there was nothing physically limiting the mare, I had just never jumped her, so we started training her. She never put much effort into it but did what we asked. When the show season ended, we gave her some time off from jumping and just recently started again. She is a different horse, moving steadily and eagerly towards every fence.
I personally think its different to say "this horse doesn't have the passion for something" or "this horse will never cross an obstacle". I see that many of the limitations that horses have are given to them by people who assume that if they can't do it, it can't be done. Its like having a child and not having faith in them. I work with a lot of children, and I can tell you that the number of parents that do something for their children the first time they say they can't is astounding. I had several of these kids at camp last week and every time they said they couldn't, I said "sure ya can" and eventually they did get it. However, their skills were definitely lower than the kids that thought they could do anything if they tried hard enough.
I have plenty of horses that don't like water but will cross it, and some that would dive into every pond if I let them. I see water crossing for some horses very similar to how I see doing my house chores. It is something that may not be pleasant, but part of my life and I will do it, it doesn't hurt me. I know the horse thinks it may be a horse eating puddle, but with the correct preperation and encouragement, any "non water crossing" horse I've had has learned to cross water.
I think that when people say "they can't", they are basically saying "I can't figure out why the horse doesn't want to and I can't fix that fear".