Examples of LEGO Rubber Bands Used For Friction Enclosure?
I personally would steer clear of a "cookie jar" setup.  The very suggestion of it's inherent qualities suggests something that wasn't meant to transport, but rather sit on a solid counter.  The rubber bands aspect seems potentially problematic as well.  Finding one that perfectly fits could prove difficult, and their elasticity would likely try to pinch in-between the tolerances of the bricks.  A rubber O-ring, being thicker and firmer, would be better suited for this task.  Personally I would opt for simple proven concepts that don't require guesswork and avoid potentially temperamental solutions.  If you did manage to figure out a working snug fit, you then would need a big gaudy handle sticking out to remove it with.  

That being said, I threw together an example of a proven method for a removable door.  It would also incorporate your original idea of wanting a snap for peace of mind.   


  

It's just a very basic design to prove a concept, one that's easy to improve upon.  One nice thing about this design is that you don't need a handle to open it, it un-clicks with just the friction of your fingers.  

If you really want a cookie jar style lid I would incorporate a few studs onto a tiled edge, similar to how Modular sections are held together.  I would suggest the lid have an inner lip to increase stability.  Again, proven methods.