You are totally right that these data is somewhat sensitive and in the best case will not be collected. In my case this would make my scientific work hard, but for the sake of privacy this would be okay for me.
The information posted to WordPress will not contain information about site URLs that use WordPress.
Are you sure? I’ve looked at the current copy of the WordPress source code at GitHub and found this interesting function wp_version_check in WordPress/wp-includes/update.php:
It sends $wp_install which depending on multisite installs is the URL of the site in the request headers. Sure, there is no evidence that the data is stored, but there is also no evidence that it is discarded and the fact that it is sent is quite telling.
So you might take a painkiller for the thought of THAT privacy issue in data collection ??
Jokes aside: It would be still nice if I could talk to somebody from www.remarpro.com who knows more about the data collection and statistics aggregation of WordPress installations.
