I've met quite a few doctors that believe in homeopathy, being a doctor doesn't guarantee a strong statistical background or critical thinking unfortunately.
They got tested and quarantined anyway... and came up negative, but are still changing PCP.
Med school requires good analytical smarts and an excellent ability to retain information, but I'm quite convinced at this point that raw analyical ability has almost nothing to do with the ability to think critically to avoid insane beliefs. It's just not something that humans come built-in with.