Seems that the dupe needs Kindness I before the triage cot can be used... and when used the dupe just lies in the cot making sick animations without actually being sick. Dupes without Kindness I skill are "ineligible" to be assigned to the triage cot and thus don't get treated when sick. Also needing 3 upgrades to treat sick dupes (access to the triage cot via medical compounding->duplicant care->improved kindness i) is a bit much. Seems to me like the triage cot should be available for dupe treatment much sooner. So I'll state that as a bug.
I added a pic showing Ellie and Harold. Ellie can be assigned, but Harold can't. Also I have no sick dupes (atm). Don't mind the puft chilling on the triage cot... That's the medbay mascot.
Steps to Reproduce
as exlained above. get a medbay > see that sick dupes can't be assigned > get a lvl 3 care dupe that can be assigned, but doesn't attend to the bed, just lies in it and pretends to be sick.
This issue has not been confirmed by a developer yet.