I was able to publish the sample Shiny app at the link you provided, set it to "Anyone - no login required", and then view and download the report as an anonymous user. The anonymous user shouldn't need an account to view or have the report rendered on the Connect server, that happens using the service account by default.
I would think there is either some additional privileged frontend/Shiny code that is requiring access, or a bug, or something else going on.
Could you post more information about the error she is seeing when attempting to download the report?
Additionally, do you have a simple reproducible example that demonstrates the error? You can scrub out your code/specifics.