iTunes says I have more photos than I really do
I have found the solution to the problem.

Quoting the solution from txforever from Apple forum.

Im not sure why is this happening, but i just know how to get rid of the prob.


  It has something to do with the Recently Deleted folder in the iPhone.
  
  You need to change the date of the phone to earlier mayb a year
  earlier as in 2014. Then go into your Photos>Recently Deleted folders
  to clear all the photo manually.
  
  Note, when you go into photo, the Recently Folder might show 0, but if
  you go into it, there is actually photo in it.