So from flight from US to Asia on a Main Cabin fare, you are entitled to two checked bags for free.
However, this Delta webpage suggests that you can get an extra checked for free if you are a Skyteam Elite (equivalent to Silver Medallion).

I'm trying to do a web or mobile check-in, and both of those channels only allow me to check 2 bags for free, and I cannot select beyond that.
I talked to Delta on the phone, and the representative just kept telling me that "they cannot verify anything" about this as I am not a "Medallion" member and they cannot see my status (pretty dumb).

Did anybody have experience with this issue? I don't want to bring three bags and pay an extra 200 dollars for this.