As discussed in our post "Why is Audius built using blockchains? Why does this matter?", Audius is built using public blockchains.
While we can suppress some data from being surfaced in the UI if a user elects to remove it (eg. see the existing track deletion feature), and remove it from systems our company controls, due to the immutable nature of public blockchains, some on-chain residual historical data may always be present.
Any deletion feature we launch can hide data, but because of this constraint someone determined to analyze the history of the blockchain could find historical references. We believe that, given the tools available today, using a blockchain is required to build a decentralized product that is community owned / controlled.
That being said, future blockchains may support pruning of residual data which is later deleted - this will become a necessity in some public blockchains soon.
You can also learn more about the Audius vision in our whitepaper: http://whitepaper.audius.co