I understand that the alternates were Amman, Cairo & Larnaca .
I just read the "Le Point" article you quoted . It does not say that Amman , Larnaca and Cairo were the alternates of this perticular Flight Plan, it says that those are [normally] the 3 airports used as alternates for a BEY flight. I would like to se the PLN before going any further.
Because to fly BEY-AMM you normally need overfly diplomatic clearance(s) unless you declare emergency and call mayday (from the start)