As an audit intern, I had some, but not a whole lot of autonomy with regards to the work assigned to me. There were only certain aspects of the audit that I could work on, as an intern. I would work on whatever tasks the team assigned to me. However, once given your tasks or certain work to do, you work on your own, asking questions as needed. So there is a sort of balance. You are given specific things to work on, but you work on those things at your own pace with the help of the others on the team.
Definitely own up to your work as an intern, but don't be afraid to ask questions or let people know you don't understand something. There will always be people reviewing your work, so the main focus is to show that you are learning quickly and can follow directions. Don't be afraid to have a pen and paper ready when a senior is giving you instructions.
As an audit intern, the degree of ownership over your work may vary, mainly because it depends on the nature of the work you are tending to. Most of the work you will come across in your internship is highly interdependent so being able to work in a team setting is crucial.
You should expect full ownership because you will be completing real work that is crucial to a determining a company's audit opinion. Your work will be reviewed, but that does not mean that you should leave mistakes. You will be given directions, and honestly many times you will not be given directions, but you should be able to give a good effort to reason through the problem then ask for help if you spend too much time on a problem area.