Sworn statements by President Trump dating back several decades indicate he has a deep understanding of campaign-finance laws, legal experts say, which could be critical if investigators ever pursue a case against him over his alleged direction of hush-money payments in the 2016 campaign.

Mr. Trump’s statements were made as part of a 2000 regulatory investigation into his casino company and in 1988 testimony for a government-integrity commission. They contrast with the portrayal by some of the president’s allies that he is...