When you are Edifixing references in No Format mode with Crossref Correction and Linking enabled and you submit a reference that already has a DOI, Edifix compares the supplied DOI to the DOI that Crossref supplies.
If they match, then Edifix removes the duplicate DOI. If they do not match, Edifix keeps both DOIs and inserts a comment, indicating that the author-supplied DOI is incorrect.
When you export your references to a structured format, such as JATS XML, you will see that the DOI you supplied is tagged with <specific-use:"author">. This tag indicates that the DOI was provided by the author.