I've never heard this before, and I can't find anything on the Delta web site or bag fee calculator that corroborates this.
The only thing similar is that FOs with an Amex that provides free bags get two bags free within the US and Canada.
I see the same thing. Fee calculator shows 1st bag free to South America and 2nd bag is $60 for main cabin tickets with and without the card. For Basic Economy fares, the 1st bag is $60 without the card and free with the card, but the 2nd bag is $100 in both cases.