If someone where to arrive at St. Mungo's with no knowledge of how they were injured, how do you think the Healers would deal with it? This person has been gravely injured by very Dark magic but has no conscious memory of what happened.
Would the Healers have some sort of spell for retrieving the memory? Would they extract it and examine it in a Pensieve?
What if neither worked? What then?
Or would they respect the patient's privacy and not go into their mind, take out their memory? Would it seem improbable for them to treat the patient without figuring out what happened?
And do you see any way of the Healers not getting to the memory, but the patient being able to do so later on? The mind is a mysterious thing, after all...