Regardless, Zack is not Genesis, whose clones attacked every Shinra installation all over the world during a two year period immediately following his service that already made him famous.
Zack was declared dead, five years pass, a large force of soldiers is dispatched to kill someone matching his description, exactly 3 men survive, and they aren't allowed to contradict the report. This guy knowing Zack isn't that plausible, Shinra Inc is a big organisation and those three guys aren't that valuable, like Zack continued to be after Genesis was "dead", probably got reassigned to Modeoheim to keep them from talking, no skin off Shinras back. Zack himself got a forced vacation after killing the supposedly killed in action SOLDIER First Class renegades too.
Cloud knowing someone who went through training with him, and Cloud knowing Kunsel, Zack's friend is not that implausible. I agree this guy wanting to tell Kunsel is kinda strained to force a Crisis Core reference but Kunsel probably the only guy they know that can pull strings to help someone with a spotty record.