I don't know if there's another name for privileging the hypothesis, but it seems closely related to anchoring, in that it involves establishing an unjustifiable "starting point" from which to search.

I crossposted the particular problem to a forum I frequent:

http://s6.zetaboards.com/EmpireLost/topic/8580222/

The conclusion in the thread is that you do best by treating based on the majority of the results at the time, but just sticking with any treatment you've already given the patient three times, on the theory that if it hasn't killed him yet it's probably right.

Unfortunately we reached this conclusion through Monte Carlo simulation, so there aren't any general arguments we can take away from it.