All three of my TBs have been pretty much this way.
My 7 year old TB mare has been used for two disabled riders (walk only because her trot is too big). She's an angel and stands stock still while they get on. One of the riders (who is in a wheelchair permanently) is suspended from a sling onto her back, the other is a big man who needs two people to hoist him up from the mounting block.
Yet she won't stand still for me at the mounting block!
My old TWH has been used in Hospice therapy. He KNOWS when he needs to be soft and gentelmanly... and he knows when there is a kid on his back, or in front of him. He is the best... and the one who sold me on the TWH as a breed...
Love it! My TB was like that as well. There was one time when he being a total d-bag with me - spooking, bucking, etc (he was having a fun old man day) and my friend was with me. She was going to ride him after I rode him for a little while. She said no way I getting on that horse. I just kept telling her just wait until you get on, he will be a different horse. And he was a total saint with her. When he got older, he was retired to a beginner lesson horse and many kids fell in love with him. He was a fantastic horse. I miss him so much.
I proud to say I've seen my OTTB behave similarly. He's a bit older and by no means extremely hot, but he can have an occasional spook and a bit of suspension. He can also cover a bit of ground for a "smaller" 15.3 TB. He has been perfect for me - just the right amount of challenge.
I was pretty confident though (with maybe a hint of nervousness) when a young girl I know with disabilities (ADHD, learning disabilities, etc) came to ride him. She rides in a local program which is on break for the winter so i offered some "horse time." He was the perfect gentleman! Didn't blink at anything, gave her the best, most-even trot he had, listened to all of her cues/aids ... I was so proud of him!
I think there are many horses out there that just KNOW. It's what makes them so special.