wp-signup.php & privacy

I would like to setup all new blogs so that they are by default private (only visible to admins, users are allowed to change privacy settings on their own).

The problem is that wp-signup.php overwrites privacy settings that are set by sitewide privacy plugin.

I tried modifying the wp-singup.php so, that privacy radio button is removed from signup-form, but somehow new blogs created via signup are still public by default.

How should I modify the wp-signup.php to force the new blogs private ?

Thanks for the help.