I think part of the miscommunication may lie in professional idiom. In medicine, all diagnosis is provisional and statistical - which both elevates "probably" to "certainly" in casual conversation, and renders most absolute statements hollow. It's just an automatic translation that has to happen: when you tell someone with a three-day sniffle that they have a cold, it's an absolute statement aloud, but in your head you have to honestly say "99.999% cold; 0.0009% HIV; 0.0001% cancer." And you have to treat them accordingly, until proven otherwise, because if you try to rule out cancer on everyone with a sniffle you're going to actually kill more people with complications than you'll ever save.

"This person has X" most of the time means "X has a strong statistical advantage in explaining this patient's symptoms, so we're going to pursue treatment for X until accruing evidence suggests we shouldn't." I guess that's not always true, given a few things that exist by definition, but it's mostly true.

And that's generally good enough, since... well, statistical masses tend to obey statistical properties.