> Many people can't deal with "You tested positive for X. We should keep an eye on it and see if it develops into something."

As I see it, this is mostly a healthcare UX problem. If a test is such that a negative result is very reliable in ruling out the condition tested for but, because of the combination of false positive rate and low incidence, a positive result doesn't indicate the presence of the condition, it shouldn't be presented to a non-technical end-user (i.e., most patients) as a positive result. It should be "The test to rule out Condition X was not able to rule it out."