Always a risky business buying a car from distance, there are no shortage of XF's around, my key advice is don't rush.
The age of the cars like any other cars this age will have things that go wrong, and while all the extras on these cars are great, it is often costly to repair, do your homework on the gadgets.
If a dealer wont give you a VIN, would worry me a little, personally I would walk away.
These cars have great engines, but must be regularly serviced, if you have none on any of the cars that would make me a tad nervous. You may want to invest in a mechanical check before purchase.
The other thing which is a problem for most manufacturers of this era and a particular issue for the 3l diesel cars is the DPF, it causes a lot of issues particularly if the car has not been driven a lot or has done mainly short journeys.
Others may call out specifics on the particular cars as mine is a petrol variant.