Most of the arrows seem to point to the occurrence of the incident. I am unsure if he remembers it, due to drunkenness.
In his shoes I might consider his best course is to explain the lack of personal apology as the result of his lack of recollection, which would make a straightforward apology insincere and inauthentic. But to admit teenage drinking, point to his usual behaviour and express regret for what she says happened.
I imagine many people would have sympathy for this over the implication that he is accusing her of lying.
On the other hand, she may be a fantasist or a manipulator. They are out there in fairly large numbers.
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