Becky knows that Alan got the car curtain (or equivalently, knows that the only way to win is if he got that, so might as well play it that way). Knowing the moves Alan was going to make, the only combinations in which he will have seen the car are bolded below:
Looking at the logic of her selections, then:
She opens A and finds a car. She then selects B or C, which will be a win for her and the pair of them in one of scenarios 1 or 2.
She opens A and finds the keys. That means a win for her if the curtains are arranged as in 3 or 4 above, but that is a win for the couple only if the curtains are as in 3
She opens A and finds the Goat, and knowing what Alan will have done when he saw the goat, she will pick curtain B, Which is scenario 6.
So she gets the keys in scenario 1 OR 2 (whichever she chose) and 3,4, and 6, a 2/3 probability. But only 3 of those scenarios match up with ones in which Alan found the car, so we are back to the 50% answer.