There might be "one true diagnosis" but there's no reason to believe that we'll have practical diagnostic tools to get it. If we need to sample the brain chemistry to diagnose a neurochemical disorder, it's probably not too useful in a clinical setting. The world makes no guarantees that we will be able to differentiate between certain situations with tools that we can realistically access and build.
Today's limits are known and undisputable. Tomorrow's limits are a promise: some promises over-deliver, others under-deliver. :)
Regardless, to bring the discussion back to the claim at hand: at all points in future, we will need the ability to reason under partial information. "Absolutely flawlessly complete diagnostics" is an asymptotic goal we get closer to but never reach. This is both very doable for a disciplined human, and very hard to outsource completely to an LLM. Treated as tools operatored by competent users, they are magical. But they can not outperform their user.