Therefore, its known narrative elements are not a part of the Doctor Who universe as we, on this Wiki, choose to define it. It may have been the basis for a similar story in another medium, however — and that story may indeed be valid.
Faction Paradox was the planned finale of P.R.O.B.E. Case Files - Volume 2. It was to be written by James Hornby to conclude the Faction Paradox/P.R.O.B.E. crossover trilogy that began with Daylight Savings and Ex-President.
However, when James Hornby ended his association with BBV Productions, the Case File was never produced, and its place on the Volume 2 DVD was taken by Legend, a trailer for The Brigadier Adventures.
In Faction Paradox, Giles would have had a video call with a bona fide live-action Faction Paradox member, one of a group of survivors of the War in Heaven. After some "mutual outwitting", Giles would have agreed to grant the Faction the lost time of England's daylight savings, analogous to the Gregorian Compact which established the Eleven-Day Empire.