This has nothing to do with Trump being "alone." Kavanaugh has been an establishment GOP tool for years.
He didn't deny being at the party, or knowing her. She was still anonymous at the time he made his statement so he couldn't.
This the trap, if, now that her name is known, you get someone else able to say there was a party that they both attended, then it tends to support her, and undermine him, even though it says nothing about the actual facts in the bedroom.