You certainly highlight the difficulty of making an early and correct diagnosis in a patient group where that diagnosis is extremely rare. The real question is how much of this is cognitive bias, and how much is a reasonable balance between the harms of overtesting and the harms of misdiagnosis and late diagnosis.
The first is absolutely the responsibility of the medical profession, and we need to improve that. And if it was obvious malpractice, the family should sue the doctor or the healthcare organization that employs them - unfortunately I think there do still exist some healthcare organizations where the only way to get them to do the right thing in future is a risk of (another) massive lawsuit.
On the other hand, it's also a good doctor's responsibility to prevent harm from overtesting https://www.newyorker.com/magazine/2015/05/11/overkill-atul-... . And the US is probably worse in this regard than other countries. In fact, a quote front hat article specifically refers to back pain:
"The researchers called it 'low-value care.' But, really, it was no-value care. They studied how often people received one of twenty-six tests or treatments that scientific and professional organizations have consistently determined to have no benefit or to be outright harmful. Their list included doing an EEG for an uncomplicated headache (EEGs are for diagnosing seizure disorders, not headaches), or doing a CT or MRI scan for low-back pain in patients without any signs of a neurological problem (studies consistently show that scanning such patients adds nothing except cost)".
But sometimes it's just bad luck, that a particular patient has a complaint that on average would not benefit from an MRI, but in their particular case, they probably would have.
Unfortunately, the only way for a non-medical person to tell if a particular patient's situation lies in the first group or the second is by suing the doctor (assuming that actually asking the doctor why they didn't do the test failed to provide a satisfactory answer). Most medical malpractice lawyers are "no win, no fee", so you can usually get a free consultation with a law firm that specialises in medical malpractice cases, and if they think there is a case there, they will take on the case. If they don't take on the case, it's usually because the care was reasonable (and therefore defensible), even though there was a terrible outcome.
None of that takes away from the pain suffered by patients and families in this kind of situations, but sometimes knowing there is a way to find out more and maybe address a specific injustice can be helpful.