Any horse can decide not to co-operate with any rider at any time, whether they are used to it or not.
A skilled rider will be able to "read" the horse and deal with the issues in a better way than the German modern pentathlete did. Its a normal part of training for experienced riders to have dealt with these types of behaviours in the past.
Getting selected to represent your country for modern pentathlon in the Olympics isn't like getting selected in athletics. There are very small participation levels, and in most countries, the sport is controlled by a small cohort of interested parties (read: parents). It is not a sport you can go along and enter; you must be invited to join a club (and you won't be permitted if those in charge of the club do not deem you of a suitable standard/background). Then you must persuade them to enter you in a competition, but in order to do so, you will have to be selected against other athletes with more pushy parents.
Standards in running, fencing and shooting are relatively poor also; athletes tend to come from a swimming background as reasonable level but not world standard club swimmers. The gold medallist runs around 18 1/2 minutes for 5k but most of them do not race in athletics regularly. Most of the athletes do not usually compete in the sports so as to improve their standards, instead they compete against each other in a very small, closed circuit of races.
When asked, a lot of modern pentathletes will complain that they do not have sufficient time to train in five disciplines.
Introducing a cycling element may reveal the poor standard of many of these athletes.
Dropping the horseback riding element of the sport because the athletes simply are not very good at it is an interesting development.