Usually when I have heard people talking about means tested versus universal benefits, they have been talking about benefits you only get in specific circumstances: for example "should child benefit be means-tested or universal?" I think your logic doesn't apply to such cases. I think if you wanted to make a universal and means-tested version of child benefit be equivalent, you would need to fund the child benefit on taxes that are only levied on people with children. The reason your example works is because you've assumed that the potential benefit recipients and potential taxpayers are the same people.
Usually when I have heard people talking about means tested versus universal benefits, they have been talking about benefits you only get in specific circumstances: for example "should child benefit be means-tested or universal?" I think your logic doesn't apply to such cases. I think if you wanted to make a universal and means-tested version of child benefit be equivalent, you would need to fund the child benefit on taxes that are only levied on people with children. The reason your example works is because you've assumed that the potential benefit recipients and potential taxpayers are the same people.