Both drivers and carriers can edit an ELD record, but the drivers are the ones who have final say in approving changes. And some things are not editable by anyone, like shortening the duration of an auto driving status.
You can correct mistakes or add information, but if you edit a record, you must include a note explaining the reason for the edit. When a log is edited, the ELD stores the original log along with a record of who makes any corrections or edits and a timestamp of when those edits are made.