Essentially, when it comes to access requests, SharePoint 2010 works in two ways. First, if you deny access to a site, list, library, or what not, the system will conceal (permission trim) that object from your view. Assuming it is within the same site collection. Second, if you deny access but have management of access requests turned on it gives the user the opportunity to request access. This is done via an email communication to the owner.
To enable or disable this feature (using a Site as the example here) simply do the following accordingly:
- "Site Actions | Site Permissions"
- Under "Permission Tools | Edit" you will see a category called Manage.
- Click on Manage Access Requests.
- Uncheck the "Allow requests for access" option and click OK.