My student (current source of most up to date gossip in Chinese!!) tells me of second-person account (so reasonably reliable -- his friend works in a local BJ hospital) instances of several people from Wuhan coming to Beijing for diagnosis and treatment of their fevers...lots just got into a car and drove straight to BJ. There is apparently a sense that the healthcare system in Wuhan is overwhelmed (appears to be confirmed by CNN crew before they had to flee Wuhan in the middle of the night just prior to the lockdown), and also only a small number of the hospitals in Wuhan have the necessary infrastructure to perform the rapid (I presume real-time PCR-based) diagnostic test...so although all patients in Wuhan need to be screened, most hospitals/clinics can't do the screening. They may send samples to secondary/tertiary tier hospitals, but that will delay diagnosis. There is also the fear that attending hospital in Wuhan (i.e. where the likelihood of 2019-nCoV is currently highest) exposes those not actually infected to highest risk, whereas coming to BJ/SH, if one isn't infected, one then won't be by the other patients in the crowded waiting rooms!
tb