That is, I'd expect that a Christian in the middle east would be more likely to have citizenship or family in a western nation than your average Syrian.

Now it could be, but 'they are being specifically targeted' doesn't immediately imply to me that 'they should be a disproportionately high number of refugees'.

That story mentions Bishops and priests who are very likely to not be Syrian Citizens, and instead be capable of just flying back to their home countries.

Why would you assume that? These are Syrian Christians who have lived their for centuries. They are no different than other Syrians other than their religious beliefs.

I'm by no means saying that every Christian will be more capable of leaving, or not be a citizen. But if 30% of Christians are citizens elsewhere, and only 3% of Muslims, then you have 70% of 10% of the poopulation as potential Christian refugees, and 97% of 90% of the population as Muslim refugees, which would make 7.4% of asylum seekers Christian, as opposed to 10% of the population.