In the proper sentence structure the noun is “Putin”. Therefore, the first pronoun refers to the “Putin”.
If I wanted to say W was a Christian I would have written:
“When Putin met with W, a Christian, in Crawford, Texas he said he was an atheist.”
In choosing the antecedent for a pronoun, a case can be made that the antecedent is the subject of the sentence (Putin). Alternatively, a case can be made that the antecedent is the nearest appropriate noun (W).
In either case: Crawford ... comma ... Texas ... comma!!!