Medicine is one area of science where there are plenty of errors, and many of them are an acceptable risk. Doctors are working with imperfect knowledge of the human body with limited time and resources. It's not a controlled lab environment where you can take your time and have unlimited tries. That's why it's sometimes known as an "applied science" rather than a "pure science".

Other than obvious malpractice cases, don't think of diagnoses as right or wrong. They are more specific or less specific. In this case the hospital was less specific because the available information/symptoms/risks didn't justify being more specific. It would be a waste of resources to be more specific than needed (e.g. we don't blood test every single person with mild cold symptoms to determine which of the 100s of cold/flu viruses they have).

I know it sounds callous but until we have some sci-fi kinda tech where you press a button and it scans your body for every single ailment known and unknown to man, we simply have to manage resources so that we can diagnose and treat as many people as possible to an acceptable level.