No,
It is the baggage policy of the marketing carrier of the first segment of the ticket. That is and has been US law since 2011. . Your baggage allowance is also, under the same US law, listed on your e-ticket receipt. It will show the fees, if any, for the first and second bags.
If for any reason the e-ticket receipt is incorrect, have it fixed now as that is what the AS agent will see at bag check.