It's not a bug but rather a weird design decision. When a person is walking towards a healthcare facility the UI will display them as being "in treatment" rather than "gravely ill", even though they still count as gravely ill and can drop dead at any time before they have physically reached the infirmary. In this way you can get deaths from gravely ill people even when there is no alert showing you have any, it all depends on their pathing and how far it is to the infirmary they choose to go to. On hard difficulty and below this is seldom an issue since gravely ill can go for quite a while before dying, but on extreme they will often drop dead.
On Winterhome, make sure to pass Radical Procedures immediately. Trying to keep people alive in medical posts with preserve life is just going to kill them, since every time the medical workers take a lunch break the patients will be evicted and need to find a new medical post, which for gravely ill on extreme difficulty will almost certainly kill them.