Yeah, but Duchess has a little surprise waiting for her next April 15th:
https://www.wsj.com/articles/look-out-meghan-markle-the-irs-is-watching-1523611800
“this means that if Queen Elizabeth II gives—or merely lends—you a tiara or a diamond bracelet, you may need to tell the Internal Revenue Service about it. Your share of the free rent for that cute cottage at Kensington Palace where you and Harry will live? Its value could be reportable to the IRS as well. If you have a credit or debit card tied to Harry’s bank account and it has more than $10,000, his account has to be reported to U.S. authorities.
To be sure, wearing the tiaras and living at the palace won’t necessarily raise your U.S. tax bill. But the penalties for not making the proper reports to U.S. authorities are often severe and can be as much as half the total assets in an account. “
Meghan has taken on British citizenship. Otherwise, you’re right, she would have to pay British taxes on her wealth and earnings, plus pay American taxes on any British wealth and earnings.