You seem to be crossing some wires here, believing the endorsement is a PIC endorsement, it is not, it is a solo endorsement. Privileges by definition is merely the ability to perform certain actions. In the case of a solo endorsement you have the privileges to fly solo and the act of flying solo gives you the privilege to log PIC.
Having the solo endorsement does not give you the privilege to log PIC, it gives you the privilege to fly solo, period. Therefore having that solo endorsement does not fall into the "privileges" in this regulation. In the case of this regulation a privilege that would permit you to log pic w/o a rating would be taking your practical test with the FAA examiner.
Be careful with wording when you get into regulations, a simple cross of the word PIC with solo with regards to an endorsement completely changes the implications. You likely know someone in your life who always took things for their literal meaning, apply that mind set to regulatory material. It isn't perfect, but it will get you on the right track 99 percent of the time, the other 1 percent is up to the lawyers digging through trial excerpts.
Midlife: Was that last paragraph a better way to put it than just read it literally every time and you'll always be right? I altered that definition slightly from some of my past posts.