Question to Dov Stein

Before going further, I asked Rav Dov Stein the following question.

At http://www.thesanhedrin.org/en/index.php?title=Korban_Pesach_in_our_time:_Questions_and_Answers, Rav Dov Stein relates to the question:

How do we know that we have someone who is really a Cohen (Priest)? Is it important?

He answers:

There are alive today Cohanim with a documented tradition of lineage that is both reliable and verified.

Please ask Rav Stein whether these Cohanim are of Y-chromosomal haplotype J1 or of Y-chromosomal haplotype J2. It would seem that at most one of the two can be descendents of Aharon the Cohen.