“All rights reserved” is not a normal English phrase, it is a “term of art” that used to be a formal requirement for establishing copyright (in some countries). According to your interpretation, any kind of license would have been incompatible with establishing copyright, which is clearly nonsense.
Under CC BY, the copyright holder gives up the right to change the terms of copying, but retains the right to determine those terms–otherwise, the copyright holder would be giving up the right to enforce the license terms.
While “some rights reserved” is a cute phrase, it has no legal meaning. As the CC licenses page says, the CC licenses operate ‘inside the traditional “all rights reserved” setting that copyright law creates’.
