Can anyone give me a good logical reason why they should refuse to justify their charges in this way? I would do far more business with them if this annoyance was removed - as it is I have to grit my teeth and accept that 40% or so of the business I am paying for will never reach me - and if any other company sent me an invoice without justifying it I'd be within my rights to refuse to pay it.
You are free to do business with AdWords or not do business with them under those terms.
Not that I don't sympathize, having experienced the same thing, but those are the facts, and it will likely be much more productive to move on to addressing another matter rather than dwelling on this one. The bottom line is --as always-- "Does using AdWords give a positive return on investment?" If the answer is "No," and you've done all you can to maximize CTR and conversions while minimizing CPC, then it may be time to try something else.
You might want to check into the cache-control settings of your landing pages; Large ISPs and corporations may be holding them in public caches, which --depending on many additional details-- may affect your logging and statistics.
Jim