The reason of concern in fractured eye socket is presence of air inside the cranium (skull) or eye socket.
This entrapped air tends to expand on ascending to high altitude (such as during air travel) & cause severe pain
In this regard, will be important to observe your partner for 2-3 days & if there is any aggravation of symptoms, it will be better to consult the Doctor.
Keeping in mind to prevent occurrence of any such event during flight, the doctor has advised him not to fly.
Wishing a Good Health. Let me know if I need to clarify further.
Thanks & take care.