Answer from VZW
Thank you for contacting our Verizon Wireless website. We are happy to assist you with your question.
You can view what applications have been downloaded from the Android Market by logging into the Android Market via the handset. Android handsets are not limited to downloading applications from the Android Market, so applications that are downloaded from the Internet will not appear in the Android Market's list of downloaded applications. As a result, there is no way to truly monitor what has been downloaded or installed without actually reviewing the applications installed on the handset itself.