Maybe this is an older posting but it makes it seem that insurance is mandatory.
Medical Insurance Requirements
"All visitors should ensure they have suitable travel and medical insurance. You should ensure that COVID-19 is not an exclusion to the existing policies.
Insurance is required to ensure that you are adequately covered in the event you develop symptoms during your stay in the Cayman Islands and need to seek treatment at a local healthcare facility. You should ensure that your coverage covers all COVID-19 related and associated medical costs and quarantine.
Visitors are fully responsible for the cost of quarantine in the event they test positive during their stay."
But under the FAQ Section they say what you said:
"All travellers will be required to attest to a statement which confirms that they have medical insurance which includes COVID-19 coverage, or that they understand the financial risks they are taking and that they have independent means to cover their medical costs, inclusive of extended accommodations. For more information, click
here and scroll down to the “Travel/COVID-19 Insurance” section."