Wall Removal - Not Load Bearing - Keep Ceiling Joists
Short answer:  If the joists overlap, than it's load bearing.  Take that wall out, and the ceiling will collapse inward.  That being said, it's really only supporting the ceiling load, not a full structural load.  But, you can't take it out without replacing it.

Long Answer:  2 Part blog I wrote for exactly this scenario.  Part 2 deals with the structural bits.  http://diy.blogoverflow.com/2014/07/kitchen-renovation-moving-to-open-concept/

Hire an engineer and get a permit.  It'll stop the insurance company from cancelling, and the city from shutting you down.

Also, find a new home inspector.