...that's not the assumption epidemiologists make. For the very simple reason that there are many "just so" stories you can tell about those still in the hospital - are they sicker, and thus there longer? Are the secondary cases, which in the case of MERS had a much lower CFR?

This is a very straightforward application of survival analysis, and those still in the hospital are "censored" observations - we know their outcome takes place in the future, but we're not sure when.

There are methods for calculating things like CFR in the presence of censoring, which will change based on what type of model you're using.