I'm not sure but I imagine it could have something to do with the way the point lamp works.
I don't think that one is more accurate than the other but that the point lamp produces these perfectly harsh shadows because the light source, as the name suggests, comes from one single point and doesn't have any dimensions. If you think about it soft shadows can only occur when the edge receives more light than the center of the shadow. In case of the point lamp that isn't possible since all the light comes from the same point and thus casts exactly the same shadow.
I hope this makes sense. In my mind it does, at least
Edit: I just realized that you are talking about the missing shadow on the base plate of the door knob In that case, I have absolutely no idea, sorry.
Edit 2: Do you have contact shadows turned on? Without contact shadows there tends to be a gap between the object and its shadow.
Blend file is here, thanks.
Also, I'm aware contact shadows aren't turned on for the point, but I'd really like to know if the default accuracy of the sun light without 'contact shadows' on can be copied for a point, area, or spot light.

– stockadelemonade Jan 15 '20 at 00:31