The claim
Correctly implemented schema is a prerequisite for rich results and helps machines understand page entities.
What the evidence shows
Google's structured data guidelines state that pages must include valid markup that follows the technical and content requirements to be eligible for rich results, and that incorrect or spammy markup can make a page ineligible. Structured data also helps Google understand the entities and relationships on a page. Eligibility is necessary, though not a guarantee, for enhanced appearances.