Epic fail. The times recorded in the billing records were the times after which a connection had been made. This doesn't include the time during which the called handset is "ringing".
Therefore, if I called my friend's mobile phone, and it rang for 30 seconds before auto-diverting to voicemail, and I listened to 2 seconds of the voicemail welcome message before disconnecting, this call would show up on the billing records as a 2-second call, not a 32-second call. Likewise, if I called my friend's phone and it was switched off, so I immediately heard a message saying that this phone was not connected, I might hear the first two seconds of that message and then disconnect. Again, this would show on the billing records as a 2-second call.
This is getting tiresome (and increasingly embarrassing)