Failed Test Run: Start new run or continue failed run?

If a manual test run is failed, should the tester start a new run to verify a fix, or should the tester continue the failed run and change the failed step to passed?

Our QA's are currently re-running the failed test and changing the failed step to passed and finishing the run. Once this is done there is no evidence a test ever failed and gaining metrics on failed runs will be a challenge.

Everything I have read says that is wrong so I'm looking for best practice advice. I believe they should leave the failed run failed and create a new manual run to check the fix and potentially pass the steps.

Thanks for advice.