Tor3 parent
.. except that there isn't really a thing such as Jewish DNA. Other than that, yes we're mostly all a mixture of people travelling and migrating and settling down and moving, and they came from all over over the centuries and millennia.
Y-DNA clades can and are associated with certain ethnic groups. Then once you confirm that, you simply need to model their autosomal DNA. And viola, you can very reliably determine if someone is Jewish, Greek, Italian, etc
There's no way it's as easy and clear-cut as that. Nothing I've seen says it is. Citation needed.