Ar100: Unfortunately what they told you is incorrect. They are a collection agency but the actual process is from the Department of Education.
"When your loan is rehabilitated, the default status will be removed from your loan, ....Also, the record of default on the rehabilitated loan will be removed from your credit history. However, your credit history will still show late payments that were reported by your loan holder before the loan went into default."
https://studentaid.ed.gov/sa/repay-loans/default/get-out#loan-rehabIf someone wanted to get the default removed I would just wait. It gets removed as a part of the process.
As far as the lates, I would just wait to see if they get removed by themselves before I started a dispute. That's just what I would do. If there's anything getting a second chance at my credit health has taught me, it's patience.