This presumes that the reason fake news is a problem is because people are spreading something they claim was said by a reputable person or organization, but is actually edited or completely false.

In my experience, the reason fake news is actually a problem is because supposedly-reputable people and organizations are themselves spreading partially or completely false information. So the information they spread would have a perfectly valid, legitimate signature—and still be just as false.

Blockchain cannot solve the problem of people lying. It cannot differentiate between what is true and what is false in the real world.