I suspect BAM to override the individual project settings to allow my computers(hosts) to be shown publicly on the WEB. How can I prevent this?

If BAM is overriding individual project settings it should warn agains this and also if I disable this setting for a project, Boincstats should respect this and stop displaying data for attached computers(hosts), as the projects do.

I noticed that the actual computer names are not listed, so I guess no harm has been done.

Hostnames and other information are only available for the host owner and the project administrator. They aren't exported via xml so stats pages don't have access to that either.