https://www.gq.com/story/scotus-kavanaugh-credit-card-debt
I think the assertion that his debts were paid off by a mysterious third party is reached through inductive reasoning but isn't established fact.
The question is: If he didn't have $200,000 in savings or liquid investments at the same time he had $200,000 in credit card debt, and suddenly that $200,000 in debt evaporated with no reduction in whatever savings and investments he had and no comparable increase in, say, the size of his mortgage, where did the money come from? Maybe he got a book advance. Maybe a rich uncle died. Maybe he sold his beach cottage. Maybe his wife sold her jewelry. But it's at least plausible that he received an off-the-books loan or even a gift from somebody who wants him on the Supreme Court. And maybe they won't expect a quid pro quo. Maybe they just know he'll vote they way they want about presidential subpoenas and indictments, restrictions on special counsels, etc., etc. It's not unreasonable to ask, "Hey, Brett, where'd ya get $200 grand?"