That's true, some hospitals may not even have the facilities to diagnose and treat sn poisoning fast enough and even if they did. It doesn't necessarily mean they'll survive.
I think this one depends on a few factors such as the individuals health such current underlying issues and I also think that when people talk about brain damage here, I think they are talking about ending up a veggie and being a burden to others for the rest of their lives so thats what they are mostly worried about because thats what most people fear, not just failure but ending up far worse from an attempt. From what I've seen, a lot more cases recover without permanent damage more times than actually getting anything that will be detrimental long term. Like this case below that I've seen.
A 22-year-old arrived at a NYC emergency department with cyanosis after intentionally ingesting 25g of sodium nitrite in a suicide attempt. A blood methemoglobin concentration was "too high to measure," suggesting severe methemolobinemia. Prior to ingestion, she had read specific instructions online for obtaining sodium nitrite and using it for suicide, including exact doses and expected symptoms prior to death. She was successfully treated with methylene blue (2mg/kg) and supplemental oxygen administration. The patient recovered without permanent injury.