There's probable a combination of reasons based on the situation:
- It seems like something Eurus would do
When Sherlock first confronts Mycroft in his house about his sister, John tells him that he was shot with a tranquilizer and Mycroft doesn't seem surprised. It's possible that she had an affinity with either narcotics (like Sherlock does) or putting people to sleep, as she does to John and then to all three of them later on.
This means that her putting an entire plane of people to sleep (except for the girl) is plausible based on her character.
- They had no reason not to believe her
Eurus caused the governor to commit suicide right in front of them, and then they witnessed Eurus killing his wife immediately afterwards. They then saw an additional three people die through the window, and she didn't even blink. Killing a plane full of people would have meant nothing to her.
She also managed to take over the prison, and then fly a drone with a highly advanced weapon attached to it, so clearly she had the means to set up something so complex.
She needed something to motivate them to continue with the game, and they believed that she was capable of setting up the plane situation without concern for the passengers, so they had no reason to suspect she wouldn't do it. It would have been as straightforward for her as setting up any of the situations that they were put in.
- They're in a high stress situation
With the pressure of the situation on top of them they wouldn't have had time to stop and process what was happening fully. They had a short time limit to complete the tasks and to try to help the girl, so they weren't able to realize that the mind game was, itself, a mind game.