Actually, it is you that have the bizarre idea. BSD licences do not permit people relicensing code without permission of the copyright holder. Copyright licences cannot do so. No copyright licence could do this.
To do this, the actual copyright ownership has to be transferred. A copyright licence is a grant of permission by a copyright owner who retains that ownership. It is not a transfer of ownership.
You don't need ownership to relicense. You just need a license which permits relicensing, which BSD does (as long as the new license is compatible, and they usually are).
It does not permit relicensing. You may use it in an aggregate work with other pieces that have a different license, including proprietary or GPL, but that does not mean your code is relicensed.
1. Its a good idea, if you are going to use licensed code that you have an understanding of the law and what it actually means when you use other people's code.
2. As the code is not relicensed you have to follow the terms. Generally for example even BSD licensed code (other than BSD0) requires that you include attribution both in source code and binaries or documentation, so you need to keep a full list of licenses and authors and list them out in the docs.
You can't take the code as-is and turn it into proprietary code. You need to build a derivative work that contains the permissive code plus some other proprietary stuff.
To do this, the actual copyright ownership has to be transferred. A copyright licence is a grant of permission by a copyright owner who retains that ownership. It is not a transfer of ownership.
* http://uscode.house.gov/view.xhtml?path=/prelim@title17/chap...