Even though Scrum was created before the Agile Manifesto, today, I do not believe Scrum truly works to its fullest potential on its own without also adopting the values and principles of the manifesto. All four of the values need to be in place to do Scrum really well, even if you are not conscious or conscientious about that fact, the fact remains, the best Scrum teams have the four values in place.
The same can be said for the principles. None of this is surprising of course since the creators of Scrum were also all signatories/creators of the manifesto itself. It actually seems to me that Ken Schwaber, Jeff Sutherland and Mike Beedle did the job of fleshing out the Scrum values and principles when they helped create the manifesto. The Scrum values are good, but for really successful teams they include the manifesto values. The Scrum principles are good, but again for really successful teams they include the manifesto principles.
If you do Scrum without the manifesto values and principles, you still get a kind of Scrum that works. It will probably work better than what you were doing before, but you will be missing some key ingredients that can make Scrum teams really soar into the stratosphere. My main point is that I would love to see some future version of the Scrum Guide actually reference the Agile Manifesto as a source for material critical to Scrum’s success. It is nice to imagine, even though I have no power to do so of course.
When I teach Scrum, I teach teams the manifesto first, always. When I mentor Scrum Masters and Agile Coaches, I advocate the manifesto as much, if not more, than the Scrum guide, at least as the source of truth for what is or is not Agile. These are two great things that are greatest together; they become more than the sum of their parts and truly define some of the best teams I have ever worked with. I hope others recognize the combination as well.