Rivers also lashed out at the hospital and officials for not treating Covid-19 patients aggressively enough, and claimed some doctors avoided treating Covid sufferers at all.
"I'm used to, when we run codes (emergency procedures), we do everything we can, we exhaust all measures to save our patients.
"Anybody that knows anything about CPR, one round is two minutes, which normally includes chest compressions and bagging them (using a handheld resuscitator).
"The patients that we coded, we were not allowed to bag them because we would get too much exposure.
"And because they were Covid positive, this hospital's policy was they only get three rounds of CPR, which is only six minutes.
"Out of all the codes that we had there, there's not a single patient that made it.
"If those doctors there would aggressively treat those patients from the beginning a lot more would make it."
Rivers also claimed the sole Covid-19 survivor on that floor was a doctor's wife who was given special treatment.
"The nurse that orientated me had one patient, she was called the 'VIP' patient, she was a doctor's wife," she said.
"They pulled out all the stops for that woman — there was nothing that they didn't do for that woman. And guess what? She was the one patient that made it out of that ICU alive."
University Medical Center told local station KVIA-TV in a statement that although it sympathises with the medical professional, it "cannot fully verify the events expressed" by Rivers.
"After watching the video, while we cannot fully verify the events expressed, we empathise and sympathise with the difficult, physical and emotional toll that this pandemic takes on thousands of healthcare workers here and throughout our country.
"This particular travel nurse was at UMC briefly to help El Paso confront the surge of Covid-19 patients."
El Paso is one of the worst-hit regions and city officials have been forced to set up four mobile morgues to cope with the increasing death toll.
The region has had its two-week lockdown extended to try to reduce infection rates.