The 76-year-old Scottish actor, best known for Succession, was speaking at a gala by the Robert F Kennedy Human Rights (RFKHR) organisation on Tuesday night where Prince Harry and Meghan received the Ripple of Hope Award.
The accolade honours exemplary leaders and the pair were recognised for their racial justice and mental health work.
Cox told Good Morning Britain (GMB) on Tuesday: “I don’t know what went on (with Harry and Meghan), but something clearly traumatic went on for the pair of them.
“I don’t think they made it up, I don’t think it’s false. I think it’s true and should’ve been rectified, and it hasn’t.”
In a recent Netflix trailer for upcoming tell-all show Harry & Meghan, the duke can be heard talking about “hierarchy in the family”, a “dirty game”, and warning “we know the full truth” in a trailer for the show.
Actor Alec Baldwin, who starred in 30 Rock, was also asked about the royal couple on the red carpet.
The 64-year-old told GMB he “tends not to focus” on the “allegations of racism” as he is a “conscious” American who realises “racism is everywhere”.
CBS Mornings presenter Gayle King said people should not “judge something they haven’t seen” when talking about the upcoming six-episode series.
King, 67, added: “I thought Meghan said it very well in the trailer. She said: ‘Shouldn’t people hear our story?'”
In the first trailer, Harry said: “I had to do everything I could to protect my family,” before Meghan is seen appearing to wipe away tears.
The duchess then said: “When the stakes are this high, doesn’t it make more sense to hear our story from us?”
Billed as a Netflix global event, the streaming giant has promised an “unprecedented and in-depth documentary series” where Harry and Meghan “share the other side of their high-profile love story”.
It features commentary from friends and family, most of whom have never spoken publicly before about what they witnessed according to Netflix, and historians who discuss the state of the British Commonwealth today and the royal family’s relationship with the press.
The director is two-time Academy Award-nominated and Emmy-winning director Liz Garbus.
Harry and Meghan signed lucrative deals – thought to be worth well over £100 million – with Netflix and Spotify after quitting the monarchy and moving to the US.
Harry & Meghan airs on December 8, with the second volume to be released on December 15.