I heard of this long long time ago. And yes it is black radish (its actually black skin but white on the inside)
I tried it, but from what I'm reading in your post I must have done it wrong because I used only grated radish without cooking it. Raw juice. OH THE SMELL!! It was ok for about half hour and then it started to smell and boy did it ever!!
On the afterthought, I guess boiling it would have been better.
However; I did get a black radish conditioner in Europe one time and it really made my hair shine.
PS. If you use egg you don't need to shampoo. Just rinse or CO.