"We usually DON'T get breakfast, just coffee," a staffer alleged, despite reports the workers get Krispy Kreme and Subway for lunch.
According to the LA Times, most of CORE's workers are volunteers who perfrom non-clinical roles for the vaccination centre, such as directing traffic and coordinating staff and patients.
Penn responded to allegations with an email which was no less than 2200 words long, published in full by the LA Times.
"Those comments, which claimed to be revealing of inaccuracies about our vaccine effort at Dodger Stadium in a news report, were in themselves not only a propagation of deeper inaccuracies, but also indulged the personal opinions of those alleged CORE staffers in a way that violates everything that keeps us whole," Penn wrote.
He adds the workers who complained should quit if they have a problem with the non-profit's operations.
"It's called quitting. Quit for CORE. Quit for your colleagues who won't quit. Quit for your fellow human beings who deeply recognise that this is a moment in time. A moment of service that we must all embody sometimes to the point of collapse. That's my job. And that's your job," he added.
He responded to the worker's criticism of Mayor Garcetti: "So, let me make this EXCESSIVELY CLEAR: With all due respect to the Mayor's official authorities and responsibilities, none give him authority to 'order' or impose directives directly on CORE staff. Full stop. His official authority is exercised at his initiative through a chain of command, that in the case of Covid vaccination programmes, he directs through the highly structured and extraordinarily well-led Los Angeles Fire Department, with whom we partner on site," Penn wrote.
CORE was founded by Penn to provide relief after the 2010 Haiti earthquake, and its main focus during the pandemic is to promote safe and efficient testing for LA residents, according to the non-profit's website.