You might be trying to create a brand new project from an existing project by only selecting to copy test entities, However in the new project that was created, you found that requirements got carried along with test scripts even though you did not check mark option for copying requirements correct?
Is this happening to the projects that have extensions disabled?
This can be verfied by checking the EXTENSIONS property of these projects in Site Admin.
This might be because the projects which you tried might had extensions enabled on them.
Regards,
Srihari