His customer configured a content deployment job that only should deploy only the public part of his site collection. E.g. consider this setup:
The job was configured to export the root site (you cannot prevent this) and the public subsite including all subsites.
During import the deployment job failed due to the fact that it tried to import content that belongs to the subsite of the private site which had not been deployed. First we thought about the common issue that the customer had links from the public content to the private content which would explain why the private content was exported as dependency. But the customer ensured us that this does not happen.
After some research we found the problem. And indeed the customer did not have any links from content in the public site to the private tree.
What was causing the problem was that the customer has created some sharepoint group to administrate content as in the private site. In the "About me" field he entered a comment like "this rights group has authoring rights on http://servername/private/subsite".
Unfortunatelly the "About Me" field which resembles internally as Notes field is a RichText field which allows hyperlinks. That caused a forward link to be created for the list item related to this sharepoint group in the User Information List.
This list resides in the root of the website and will be exported and deployed as well. That on the other hand causes all dependencies of the items in the user information list to be deployed - including the /private/subsite site.
To resolve the problem it was necessary to edit all affected sharepoint groups and remove hyper links to the parts of the site which should not always be exported.