However, in fairness, Combined Training and Jumping are the two equestrian sports where they aren't buying access and middle class riders do routinely compete at the Olympics. For example, it takes enormous talent, lots of training and incredible guts to ride a cross country course at that level. That is one sport you need to see in real life, up close and personal, to get a sense of the level of talent and risk. The jumps cross-country are enormous and not on "groomed" footing. And they are solid: mistakes can be deadly. You stand by one of the jumps and look up at the horse soaring well over your head and you begin to get a hint of it. (My first teacher wanted me to go into combined training, which was his first passion. I had the talent, but frankly lacked the necessary guts. As a teen with a crush on him, I would jump whatever he pointed me at, but that wasn't going to be real practical over the long haul, lol.)
Furthermore, thoroughbreds excel at it and are relatively low cost; gifted middle-class riders can pick them up on the cheap from the backstretch of any track. They are the (relatively) slow ones that prefer jumping to racing.
Dressage is a different story, for a number of reasons too lengthy to go into here. Although you don't have to be a 1%er to compete at the Olympic level, these days you do need to find one or more to sponsor you. That, in itself, is a specific talent that should have no bearing, but unfortunately does.
When I was young and middle class, I rode with a top international trainer and fully trained horses (called schoolmasters) to learn on, without having to buy that access access.
These days, young, aspiring riders have to buy, at prices that would buy a house, schoolmasters to learn on.
If you research deeper, however, you will find something else. Those people are able to buy access, but they aren't able to buy medals.
That is why the US and the other countries you mentioned are never in the medals in Dressage. They won't be this year, either. The Romneys can buy all the German cast offs they want; Germany's best stays in Germany and represents Germany. 
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