It was reported earlier today that Willis was concerned he would be unable to pass on the music downloads he has purchased to his daughters, Rumer, Scout and Tallulah, after he dies.
This is because Apple's terms and conditions for iTunes currently state that someone is unable to include the downloads in their inheritance as they are borrowed under a specific licence and not technically owned.
However, in response to questions about the story posted to her on Twitter, US model and actress Heming tweeted: "It's not a true story."
The story may be false, but it has stirred an interesting debate on something that many iTunes users may not know; that even though Apple offers DRM-free downloads, it only actually sells a licence to play the music on up to five devices, rather than complete control over the file.
This means that a big music collection on iTunes cannot be legally passed on to anyone else, such as in an inheritance.
Fabio Torlini, the vice president of cloud at hosting company Rackspace, said in a statement earlier before Heming denied the story that many people are starting to think about how to hand on their "digital treasures".
He pointed to recent research that indicated the digital contents of people's "virtual attics" is worth an estimated £2.3 billion.
"As people put more of their digital treasures online, including music, photos, e-books and passwords to email accounts, thinking about how to pass them on to loved ones becomes more urgent," he said.
Torlini added that 11% of people surveyed said that they had included passwords to their digital assets in their will, or were planning to do so as a way to ensure that the content was not lost forever.