If 700 hundred people leave on a boat, all fully vaccinated, and if 100 of them develop COVID while traveling, the denominator here is 700 because you have an isolated population. The infection rate on the boat is 100/700 or 14%.

This actually happened:

HMS Queen Elizabeth: Covid Outbreak On Navy Flagship, BBC, 14 July 2021

The BBC has been told there have been around 100 cases on the aircraft carrier, which is part way through a world tour (a quarter of the way through a 28-week deployment).

You would not apply a national rate, that is, you would not say that developing COVID on the boat would be rare given a national rate of, in the US, 125,000/164 million (Americans who have been fully vaccinated) or 0.076%. If that rate applied then you would expect maybe one person on the boat to get COVID.

When I see someone using the entire vaccinated population as the denominator, not describing what percent of that population was exposed, or a breakdown by age, comorbidities, or other risk pressures, I think they are being disingenuous.

They are misrepresenting the data so they can say getting COVID is rare if you are vaccinated. I would not say it is rare.

CDC Study Shows 74% Of People Infected In Massachusetts COVID Outbreak Were Fully Vaccinated, CNBC, 30 July 2021

The denominator is everything.