When Bourne reaches Vegas airport, Heather clears his passport for him which prevents him from being detained at immigration. How did Bourne know that he would be cleared?
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He didn't. Watch his body language in that scene - he is tense and then surprised.
However, he had no choice but to trust Heather Lee and so he went. Seeing previous Bourne movies would show he would readily make himself a plan B if he encountered a problem.
