You absolutely can download individual issues via USB. Go to Amazon.com, Your Account, Manage Your Kindle, scroll to the Your Active Kindle subscriptions section, click the plus icon on the left side of what you've subscribed to, and click "Download to Computer." Moving it to the Kindle is left as an exercise for the reader.
You can select back issues from your subscription to download, but only for a little way back. Right now with the Philadelphia Inquirer I can only go back to December 8