You can set the URL you see when you go to the Accesspoint and click on "Open with IE Plugin". Use that URL instead of the Accesspoint for each user.
If section access is properly configured with NTNAME, and documents are filtered by user (Settings menu, Document Properties, Server tab, "Filter AccessPoint Document List Based on Section Access") the Accesspoint will show only the documents where that user is.
You can use instead NTFS permissions, so if the user is not in the security list of the document, it will not be shown to this user.
But if you go to the AccessPoint you need to click on the document you want to see to open it, or use the direct URL instead.
Hope that makes sense.