I can offer a little insight on this one. I no longer work for Orange since the merger, however until the middle of last year I was the Billing Test Manager. As such I managed the testing of tariffs, investigation of live incidents and also the regulatory billing testing required by OFCOM and BABT.
For the regular testing of billing and charging they use an automated call generation tool. They have a number of calling "robots" that are dotted around the country. These make calls, texts and data sessions that number in the hundreds of thousands per month. The system is capable of detecting any discrepancies with the billing system to within 1/10th of a penny. Calls are easy to check the accuracy of as the system can call machine to machine and measure the duration on both the inward and outward leg of the call. Texts are also easy as they are very definite in their nature, made up of single 160 character messages. Data on the other hand consists of many elements, the actual page or item you are downloading, but also contains uploads for requesting the page, page headers and also retries for when the page is taking too long or data lost in transmission. Therefore what is measured at the handset isn't always the same as that which is measured by the network for the full transmission. For testing we would download a specific file and check the amount of traffic billed.
As for asking Orange to disclose exactly what sites you have accessed, this is particularly tricky and treads into quite a murky area. For billing purposes it is perfectly fine and legal for any network provider to collect a certain amount of data, this can include time, date number called etc. Texts are the same. For data they can only disclose the time, date and amount of bytes. Any more information than that would essentially be the same as listening to your calls or reading your texts. To do so would require a warrant and disclosure under RIPA.
Hope this helps.
Paul