Interact as in having a wrapper application to integrate with the current review/rating system. Posting/publishing a review, rather than showing already standing reviews.
I guess I've answered my own question according to Josh's response, however I assume it's a simple database that is appended to once a user sends a review, something that isn't hard to integrate with.
You can change the email address in the settings of the review app to be sent a notification when a review is posted, let's say 'firstname.lastname@example.org'
Write some code that monitors that email inbox, parse the new emails as they come in and store the data (title, description, email address of the user, timestamp, etc) in a database. Once the data is in a database you can do more with the data from there, but it's still not the same as having an API, but it's something.
I have been toying with writing my own rewards app (so I don't have to pay for it) - I have already written an integration with Mandrill to send automated review emails after an order is delivered. I would then like to reward a customer with points for writing a review. You can't get that sort of functionality without paying monthly fees for apps, and that isn't something a boostrap start up can afford when starting out, but is critical to driving conversion on websites.