The story might be true. He might have convinced himself that it was bitachon when it was really something else.
The story is told that the Vilna Gaon heard that a relative went to a doctor, and was unhappy about it. He was asked, “does the peruke not say v’rapo yerapei”? He answered, “yes, but I’m disappointed that someone from our family is on that lower level of bitachon “.
Needless to say, it’s been several generations since anyone was on that level. In concept, though, v’rapo yerapei is permission, not an obligation.