Good question!  They are both true.  The former is just being extra safe.  Typically, it's okay to store your board flat.  Especially if inside where there is controlled humidity and temperature.  Most of todays modern builds have strong camber so thay are really not affected.

Hey, no problem.  If a board loses it's camber, it will not distribute the pressure along the base and edges as evenly.  It will also lose the snappy feel.  Not the end of the world, but not optimal performance either. 

Peace Out!