Boomerang,
Russia doesn't have the firepower to prevent coalition aircraft entering Syria and if they did they would be on a death wish if they endangered any of our aircraft.
As to being invited into Syria, I don't think the coalition cares. There is a war on against DAESH and we are even debating on deployment of troops.
At the end of the day, we don't care if the Syrian border is closed. What does that mean? Absolutely nothing because it is better for it to be closed from a Security perspective. Who in their right mind wants it open?
And no NATO did not tell Turkey to shoot it down. NATO only supports Turkey's right to defend its airspace and this is in NATO's interests. It's not like Greece which basically encourages Turkey to violate more. Turkey's actions provide Russia with significant discouragement.
We will see in the near future but the West won't be budgeing and Pootin has his hands full unless there is a Peace Treaty and for that to happen, Assad will have to go!