If you are concerned about not providing the logs and want to try to cover all your bases, there are methods of exporting your Facetime call logs and/or iMessage from iPhones using 3rd party apps to .txt or .csv that you could convert to documents or spreadsheets (MS office or Google docs) and then print out. I'm a new user on this forum so I can't post a link but if you google it, you will find it.
I did a similar operation using Skype where I copied the whole chat log into a .txt file and pasted it to Word .doc file. From there I selected 10 pages and printed them out. iPhone will be a bit tougher but the information is there, you just have to find a way to get it out of your phone and onto a document.