What's the story?

What do we make of this business about Damian Green's computer?  Long story short - ten or so years ago the police were investigating  information which was allegedly being "leaked" from the Home Office.  Green - then shadow immigration minister - was arrested as part of this investigation and documents and computers were seized.  In the event, no charges were brought against Green, but the police are now saying that back then pornography was found on his computer.  It matters now because he is currently the de facto Deputy Prime Minister.  The important words in the police's statement to my mind are "on his".  "On" first of all - from what I read there is no suggestion that pornographic images were found on the hard disk, but rather that the browsing history showed that the computer had been used to access pornographic sites.  Which brings us to "his".  To what extent was it his computer - how many other people had access to it?  I've not seen the answer to that question, or even any indication that it has been asked.  So is this all froth and bubble and no substance?