Early man faced a lot of dangers, and the fight-or-flight response evolved to help them evade or battle those dangers in order to survive. Today, it's what allows an ordinary Joe to rush into a burning building or a mother of three to lift a car off of one of her children -- a phenomenon known as hysterical strength.
The Zee Drive trial subscription limits the amount of data you can upload or download through your mapped drives in any given 24 hour period to 5,000 file uploads or 3GB of data and 10,000 file downloads or 5GB of data. Zee Drive requires Microsoft .Net 4.x and Windows.
The 32,000 limit you are referring to is the number of objects in a database, not a limit to the number of records. The record limit on an Access 2003 table is only limited by the database file size, e.g. 2 Gbs minus the space for System objects. For more of the limitations of Access 2003 please see: Access Specifications.