Piwik makes a lot of outgoing connections. There are some options to disable all these connections, but there's no central place where to look at to know easily what to do to disable all outgoing connections.
Some things that are needed:
Thanks for the feedback! There is this FAQ http://piwik.org/faq/troubleshooting/faq_16646/ and this issue https://github.com/piwik/piwik/issues/6324