how they even know WHAT train he was on. they know he took the 1,a, and L but not what train and what care he was on
They could pretty have a certain time frame. For example, if he got on the train, let's say at 5:30pm heading downtown, the MTA could go back & find the interval that the train made out of the terminal & put that train consist in the yard to be cleaned. The train itself necessarily wouldn't be the problem, but the passengers who were on said train, it would near impossible to find everyone that was in that train car with the doctor.
And Ebola news aside, I wouldn't sit on those benches in the train stations either, just a heads up.