Had this picture of Anthony Ainsley as the Master and Tom Baker as the Doctor not been adulterated, we couldn't use it for Toobworld fanfic. It is already a moment locked in Prime-Time. (It happened in the final chapter of the story "Logopolis".)
Photoshopping has become a matter of course online now and Toobworld Central has to keep up with the times. So we can see this as being a pozz'ble event in the life of the Doctor, but it's not definite. We accept the picture as a launch for fanfic, but not declaring it as actually having happened.
For anyone wanting to use this picture to inspire and illustrate any fanfic story based on it, I hope you'll make sure to send me a copy or at least the link so that I can read it online.
Could they have had a run-in with The Wire in its escape from custody? The Wire could have stolen their faces but in making its escape from the Atraxi, it had to jettison them too quickly. This would be why they were returned to the wrong bodies.
Can you think of a better reason for what happened within the TV Universe? Write it up and share it with me!