The Aquaman actress, 34, denied affairs with the Tesla founder and actor as she gave evidence in Johnny Depp’s libel action against The Sun newspaper.
She insisted she had only been in communication with Mr Musk in 2016, rejecting suggestions the tech billionaire visited her at her Los Angeles apartment the year before whilst Mr Depp was away.
Eleanor Laws QC, representing Mr Depp, read to the court text messages allegedly between Ms Heard and Mr Musk from May 22 2016, in which she tells him that she is going to obtain a restraining order against her then husband.
This is the day after an alleged incident at the Eastern Columbia Building in LA, where Mr Depp and Ms Heard lived, in which the actress claims Mr Depp threw her mobile phone at her, hitting her in the face – which the actor denies.
Ms Laws said Mr Musk offers to “arrange 24/7 security for you (Ms Heard)”, adding: “The offer would stand, even if you never wanted to see me again… anyway, sorry for being an idiot. The radio silence hurts a lot. It only matters because I really like you.”
The barrister referred to evidence given by Alejandro Romero, a concierge at the Eastern Columbia Building, who said he saw Mr Musk visiting Ms Heard “when Mr Depp was in Australia”.
Ms Heard responded: “He’s wrong. I wasn’t even in communication with Elon until 2016.”
In his written witness statement, Mr Romero said: “From March 2015 onwards, Ms Heard was visited regularly late at night, at around 11pm to midnight, by Mr Elon Musk.”
The concierge claimed that after he had made a few visits, Ms Heard gave Mr Musk his own garage remote and a fob to the apartment, owned by Mr Depp.
During her cross-examination of Ms Heard, Ms Laws also asked the actress about Mr Franco, saying: “On the topic of what you say about his (Johnny Depp’s) jealousy, you mentioned in your statement that James Franco was someone that Mr Depp was accusing you of having an affair with and he was quite wrong about it.”
“That’s right,” Ms Heard replied.
The court was played CCTV footage of her travelling downstairs in the lift at the Eastern Columbia Building on May 22 2016 at around 11pm, before travelling back upstairs shortly after with Mr Franco.
Ms Heard confirmed that the man in the footage was Mr Franco.
It shows Ms Heard, in a long coat, get into the lift, followed by Mr Franco, who is wearing a baseball cap and backpack.
She moves to stand next to him and the pair stand close together, appearing to talk.
Asked by Ms Laws: “Are you trying to avoid being seen by the camera there?”
Ms Heard replied: “We were talking. He was saying to me ‘oh my god, what happened to you?’
“He saw my face… when I let him in. He saw my face and he said ‘what the f***?’”
Ms Laws asked: “That’s not secretive talking on that camera?”
Ms Heard said: “Yes, it’s discreet.”
