look up from longman dictionary of American English rang, sang,

It is clearly to me is the same vowl as bat.

I also compared "saying" with "sang", There is a clear distinction of [ei] and {ae] from Longman dictionary as i listened a few times.

The youtube one is incorrect to general american dialect. It could be due to a region dialect. I noticed one of the best readers here didn't pronounce "man" as the dictionary pronounced. I suspected he might be in Vancover area, and it could be a dialect in that area since I met another person somewhere speaking like what he did.