This maybe a case of differences across academia resulting in an unclear question. I have never heard of two universities awarding a single degree and would not term such an activity as a "double PhD". I did my PhD in a strange department in the US that was split across two universities (so very similar to what you are describing). At the point of defending our theses we had to choose which university our degree would be from and we had to format our theses according to the policies of that University. There was no option, nor any discussion amongst faculty or students, to get a jointly awarded degree.
If this jointly awarded double PhD is in fact different from getting two PhDs, I think a clearer description would be very helpful for US and UK academics.