Does anyone think the particular way the inside of a person's mouth is shaped will influence the way air passes through and this, in return, will influence the sound of the harp and perhaps explain why some people can bend notes easily and others have a harder time?

Just wondering!

Absolutely not if you are referring to physical anatomy. But the further you get the harmonica into your mouth and the lower you drop your jaw to create a large oral cavity, the better.

The corners of your mouth are actually what block the two surrounding holes when attempting single notes. This will work when you drop your jaw (slide it down and back slightly) and then use your index fingers to press in the corners of your mouth (a la "fish face"). Once the corners of your mouth are covering the two surrounding holes, push the harmonica into your mouth. The slight pressure pushing in will hold the corners of your mouth to the harmonica.

See first color photo example-
http://www.harmonicalessons.com/members/sinnotes2.php

Hang in there, it just takes practice good single notes and a full "professional sounding" tone. Check in a mirror to really see what you are doing with your mouth. Let me know if this helps.

Play on,
Dave Gage