A decision includes interpretation of the facts, and that interpretation is colored by the individual's beliefs, which means there is faith involved in decison making.
Yes, it is a decision, not a choice.
A decision and a choice are basically the same thing. The bartender makes a decision that the ID is real or fake. That means he is making a choice to believe it is real or fake.
The only choice he can make is to ignore the facts, as in the earlier bribe example.
Providing there is a hologram on the ID, and providing he has faith that no one has found a way to duplicate the hologram, and providing that he believes the person holding the ID is the same person pictured on it.
I'm going by the evidence of your use of the word in place of other, more appropriate terms.
You are going by your interpretations of what I've posted, and those interpretations are colored by your beliefs.
If you let it. The bartender has no beliefs involved though. He doesn't have to "believe" an ID is fake. He has specific criteria that tell him it is.
That means he is making a choice to believe it is real or fake.
No belief. It is or it isn't according to the criteria.