To this end: we can (WLOG) make the degenerate observation that a property of all doctors is that they are doctors. Then the original chart just shorthands away whatever conjugation of "to be" is proper in the outermost bubbles, and does indeed map properties of the various groups.
It's still not a Venn diagram. A Venn diagram labels regions, not points in the regions. The diagram could be made correct by placing little dots in the intersection regions to show that these are points in the intersection, whereas the outermost categories are sets of properties. But it still wouldn't really be a Venn diagram :)
