I doubt they would meet the qualifications outlined on that very site which I suspect they went to and tried to arrange a test:
Below outlines the criteria for when a New Yorker is eligible for diagnostic COVID-19 testing. This criteria is subject to change based on test availability, testing capacity, and for public health reasons.
Diagnostic testing for COVID-19 shall be authorized by a health care provider when:
An individual is symptomatic or has a history of symptoms of COVID-19 (e.g. fever, cough, and/or trouble breathing), particularly if the individual is 70 years of age or older, the individual has a compromised immune system, or the individual has an underlying health condition
OR, An individual has had close (i.e. within six feet) or proximate contact with a person known to be positive with COVID-19
OR, An individual is subject to a precautionary or mandatory quarantine
OR, An individual is employed as a health care worker, first responder, or other essential worker who directly interacts with the public while working
OR, An individual presents with a case where the facts and circumstances – as determined by the treating clinician in consultation with state or local department of health officials – warrant testing
OR, An individual is included under other criteria set by the NYS Dept. of Health based on an individual's geographic place of residence, occupation, or other factors that the Department may deem relevant for COVID-19 testing purposes
OR, Any individual who would return to workplace in Phase 1
If they wanted to come to the DR, they would likely have to pay out of pocket for a CV19 test if their insurance doesn't cover it. As you can see from the above, it is not just walk in and get a free test. You have to meet one of the above criteria. They could lie about being in close contact with someone who had CV19, I suppose. My real point is that getting an Affidavit of Health is going to be a nightmare for many if that is required to enter the DR as a tourist.