The first cars arrive at Hard Rock Stadium shortly after 4am. It is three hours until sunrise, and five before the state-run coronavirus drive-through testing station opens its gates, but the early arrivals, some coughing and feverish, all wearing face masks, want to be sure of their slot.

Even so, some are out of luck. With a daily capacity of only 400 tests, it takes authorities fewer than 120 minutes to exhaust their limited supply of throat swabs, and those at the back of the queue – after hours waiting in temperatures close to 90F – are sent away to try another day.

Meanwhile, over on Fisher Island, a swanky enclave for the super wealthy barely 15 miles away, and where the average annual income is $2.5m, it is a different story.

Island managers’ controversial private purchase of thousands of rapid Covid-19 blood test kits from the University of Miami’s health system means there is no need for any resident to leave the island or wait in line with the public at large.

Here, there is time for a leisurely breakfast and a stroll around the 216 acres of America’s richest zip code before stopping by an air-conditioned medical office for a guaranteed swift blood draw. While those fortunate enough to have received a test at the stadium must wait several days for a result, the instant nature of the in-demand blood antibody tests means islanders learn of their situation within minutes.

“It’s no different from Disney World, where you can buy that special pass and cut in front of the line for 30% more,” said Dr Jay Wolfson, professor of public health medicine at the University of South Florida.

“The control and distribution of essential resources in the US economy is by design, structure and culture driven by those who have such means. The Fisher Island people can cut a deal on the side with the University of Miami and they get to take care of themselves.”

This juxtaposition of the haves and have-nots has sparked a backlash in Miami-Dade county, a coronavirus hotspot whose 7,863 cases by Wednesday lunchtime were more than double that of any other county, according to the Florida’s department of health.

A lack of accessible testing for poorer and more vulnerable members of society has caused friction between local authorities and the state, and the county mayor, Carlos Gimenez, announced this week that in-home testing would be available for some residents unable to reach drive-through sites.

Alberto Carvalho, superintendent of the Miami-Dade school district, the nation’s fourth-largest with more than 350,000 students, vented his frustration on Twitter at the privilege enjoyed by Fisher Island’s 800 families.

“Fame, fortune, power, or position should not in any way allow anyone to skip the Covid-19 test waiting line,” he wrote.

Some criticism is directed at the University of Miami health system (UHealth), which recorded a record $217.2m profit in 2018, financial records show. UHealth accepted an undisclosed amount of money from Fisher Island for thousands of the blood tests, the Miami Herald said, available to every resident and worker regardless of whether they were showing symptoms.

A UHealth spokeswoman, Lisa Worley, did not answer specific questions from the Guardian about the arrangement, but sent a statement admitting the episode had prompted introspection.

“We understand it may have created the impression that certain communities would receive preferential treatment. That was not our intent,” the statement said.

“One of the first confirmed cases of coronavirus in Miami-Dade county was on Fisher Island, more than half of the population is over 60 and many residents were returning from the Northeast. These factors, at the time, were taken into consideration when the request was received.”

It added that UHealth would be “revising its process for reviewing testing outreach requests”.

UHealth has been collaborating with Miami-Dade county on an unrelated community testing programme, Worley said.

Nobody was available to comment on Wednesday at the Fisher Island club, which according to Business Insider charges annual membership dues above $22,000 on top of a quarter-million-dollar initial fee.

At the Hard Rock Stadium, temperatures reached 92F on Wednesday. The Florida association of public information officers, which has been handling media inquiries for the site, warned again of long wait times and advised drivers to have a full tank of gas.

Wolfson, the public health professor, said the drive-through system still excluded many at-risk residents, including the elderly and disabled, and racial minorities shown by data to suffer higher rates of infection.

“Maybe they can apply for jobs on Fisher Island,” he said.