Definitely sounds like something in the pan. Not a complete blockage just enough to slow the rate the water drains. Baby wipes, blue roll, something in that line i suspect. You should be able to remove the pan and cistern without removing the boxing, just make sure the pan con is in good condition and stays put when you slide the pan back in.
Although if he is grumbling about price just tell him to do one!
I reckon you are right and I reckon the customer knows something too but doesn't want to say. \he kept saying how 'maybe' someone has put something down there. So I reckon they put anything down without a care in the world.