Both of you are in agreement only using different words. - The UK or anyother VWP or long form US visa holder who enters via commercial
airline - has a valid visa or the airline would not have let them on the airliner at their departure point. There is a massive monetary fine to any airline who fails to ensure that their passengers are in possession of a valid visa prior to boarding the airliner. And if one slips through the airline not only has to pay the fine but must take the person back to their departure city and eat that cost (over and above any money
their got from the round trip ticket the passenger purchased).
Entering any US port (with includes airports) on anything other than the approved airlines, approved cruise
ships, ferries, etc. (and specifically does not includes private sailing vessels) requires a long form pre-approved Visa which it very costly and time consuming to acquire. The "ferry option" between the BVI and USVI is well known and used extensively by cruisers coming up island and heading west to gain access to the USVI and Puerto Rico
. It is also technically available heading east from the Dominican Republic
but unfortunately the Ferries only leave from Santo Domingo and are very expensive so nobody uses it.