Many places have out of date documentation — you should correct or update that information as you go through your first few months. This generates real value for the company/team and helps solidify your understanding of how things work. You can also form useful contacts since you may need to seek out the institutional knowledge from senior employees in order to form this documentation.
Expecting the newest member to update the docs seems to be pretty common but has always struck me as pathological. The person with the worst understanding and least perspective is the one who's expected to teach it to others.
In my mind this is just an extension of good software engineering practices: if your system has a bug or error which requires development time to fix you should find and fix the root cause of the error. Similarly if you are onboarding and you are blocked by undocumented processes you should go out of your way to find out the root cause of the issue and fix it for future developers.