Does that mean that the examiner has to sign it on behalf of / as the instructor? Or does the student get the authorisation before they leave home base?
From a practical point of view, I would imagine that the instructor signs the authorization for both flights (to and from the examiner airfield) as one document. I mean, you don't sign/carry three separate forms for the three legs of the QXC, do you? But as said, I would add the condition (and put it in writing) that the student phones the instructor before flying home.
And I would insist that the student somehow takes time to unwind after the exam. Have lunch, go for a walk, read a newspaper, whatever. But spend at least an hour away from the aircraft and from the whole flying environment in general, to let the adrenaline wear off.