Why did the US department of state tell me UK citizen cannot enter the US after 15-day Carribean stopover?

I am almost certainly sure that the US Citizens Distress Hotline was confused, either with the question you asked or were unsure of the information themselves.

The US Government page clearly states traveling from these countries is possible after not being there for 14 days:

After arriving to the United States from one of these countries, CDC recommends that travelers stay home and monitor their health for 14 days.

This clearly shows that passengers who have been in these countries (more than 14 days ago) are still allowed.

I have a feeling that the US Citizens Distress Hotline was confused with the rules for people who are exempt from this 14-day rule. The exemptions are published under section 2 here.

The ESTA FAQ seems to confirm that after a stay of 14 days in Bermuda ('United Kingdom, excluding overseas territories outside of Europe,'), a holder of a valid ESTA may enter the United States.

What if I am a passport holder of a Schengen country with a valid ESTA but I have not been present in a Schengen country within 14 days of my travel to the United States?
Travelers are subject to the Proclamation if they were physically present within the Schengen Area during the 14-day period preceding their entry to the United States. This prohibition necessarily includes direct travel from, and transit through, the Schengen Area within the 14 day period.

If you have not been in the Schengen Area during the 14-day period preceding entry, and you are not departing from or transiting through the Schengen Area during your travel to the United States, then you are not subject to the Proclamation.

What if I am a British Citizen (GBR) and/or an Irish passport holder with a valid ESTA but I have not been present in a Schengen country within 14 days of my travel to the United States?
Travelers are now subject to the March 14, 2020 Proclamation if they were physically present within the United Kingdom, excluding overseas territories outside of Europe, or the Republic of Ireland during the 14-day period preceding their entry to the United States. This prohibition necessarily includes direct travel from, and transit through, the United Kingdom, excluding overseas territories outside of Europe, or the Republic of Ireland within the 14 day period.

If you have not been in the United Kingdom, excluding overseas territories outside of Europe, or the Republic of Ireland during the 14-day period preceding entry, and you are not departing from or transiting through the United Kingdom, excluding overseas territories outside of Europe, or the Republic of Ireland during your travel to the United States, then you are not subject to the March 14, 2020 Proclamation. However, you may be subject to Proclamation 9993 applicable to the Schengen Area if you have been physically present in the Schengen Area within 14 days of travel to the United States.

Sources:

• Official ESTA Application Website, U.S. Customs and Border Protection

I have no idea why the Department of State gave you that answer, but you were asking the wrong people. It's rather as though you called your local fire department's fire safety inspector to find out whether you can get a license from the health department to operate a fruit stand. They really shouldn't have given you any answer at all:

1. The office of US Citizens' Crisis Assistance is not concerned with entry requirements. Its job to help US citizens, but the question you're trying to answer concerns only people who are not US citizens.

2. The Department of State does not operate immigration control at ports of entry; that is the responsibility of the Department of Homeland Security. While the State Department does issue visas, its employees are not necessarily trained on the terms of the Visa Waiver Program, and even for travelers with visas the final decision lies with Customs and Border Protection, an agency of DHS.

Try calling an office of Customs and Border Protection. They are the ones who actually decide whether someone can enter the US. Their contact page links to a map allowing you to locate ports of entry by state.