I was going to ask the same question. It seems an assertion that would be difficult to support. Maybe with lots of DNA analysis. The Medes were the most populous tribe of Iranian peoples. The Pars tribe became dominant under Cyrus the Great, and the land became known as Persia. Did the Medes stay separate? Or did they intermingle with the Persians and others to the point that it could not be said they still exist? I don’t know, but I didn’t see any support for the claim in this article.
Kurdish is supposed to be an ancient, less Arab, Iranian language, but I always thought that was because their mountain region was less subject to total conquest, and they were left alone when Arabs imposed themselves.
They do some interesting stuff with genetics recently. I don’t think they have it all quite nailed down particularly with the complex issues of historical migration, but its getting there
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1274378/