Hope we find a UK person to shed some light. I have a similar situation with one from Greece (but she has a 10 year visa in her old passport so I think we got lucky, she just needs that and her current passport with an expiration date of over six months) and one from Cyprus.

When I went to the link, travel.state.gov referenced under
"Specific requirements must be met for these Nationals to qualify. For more information visit: Travel.State.Gov.com"
it takes you to the Visa Waiver Program. The problem with the VWP is it doesn't work for private/charter boats. So even though they make you think you don't need a visa it only applies to commercial carriers like airlines and ferries. I think that is the specific requirement they mention in your link.

Of course, I may be wrong. That's just the way I am interpreting it.