In the case here, the act of receiving presents serves as a general statement about Christmas. To my mind no specific Christmas is understood here; instead all Christmases seem to be the explicit understanding.
Thus, following your grammar explanation, the more correct grammar choice seems to be "à".
I think this remark found in the lesson applies here:
- when you're talking about the very day of the celebration (on Christmas Day), you use le jour de + [célébration].
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