On Thursday, in an interview with The New York Times, Mr. Musk was asked if drugs were involved in his market-moving tweet. “Absolutely not,” he said.

[Mr. Musk spoke about the struggle to cope with the pressure of his jobs: “I’ve had friends come by who are really concerned.”]

And then there is the question of whether they had even met.

In an interview with Business Insider on Monday, Ms. Banks said she “saw him in the kitchen tucking his tail in between his legs scrounging for investors” after his tweet about taking Tesla private, adding, “He was stressed and red in the face.” On the same day, Mr. Musk told the website Gizmodo that he had never met Ms. Banks or “communicated with her in any way.”

But they did lay eyes on each other, after Mr. Musk emerged from his workout that Friday morning.

Ms. Banks had arrived in the predawn hours, invited to the house by Grimes, people familiar with the sequence of events say. The two women had announced plans in June to collaborate on a project, and studio sessions were scheduled for that weekend, Grimes’s representatives said.

But there was a miscommunication over the plans, Grimes’s representatives said, because Grimes and Mr. Musk had instead made arrangements to go out of town.