Simply put, use the API provided to send/receive funds from your wallet. Don't act as a mediator for transactions involving a wallet which don't belong to you. Should you wish to do so, they have a third party authorisation tool which sets the app permissions by the other users so you can have a sort of control over their wallet.

To simplify it further, it is similar to using your google account for signing up on other websites. You will be shown a pop-up to grant access.