The way I've seen this done is to have a set of statuses in the Request with the same 3-letter key as the Project.
e.g. If your Project's "Reject" status 3-letter key is REJ, you create Request status that has REJ as the 3-letter key (call the status what you want, but we would call it something like "Project:Rejected"). Equate it to whatever status you like (closed would be my choice). Lock and hide the status so that users are not able to see and use it.
When you change your project's status to rejected, it will change the request status to project:rejected for you.
I'm sorry, I don't know what the notice is about you needing access to make the change.