Thinking through your situation a bit more, I imagine that the issue being raised stems from the DFW-SFO leg possibly being considered a separate flight, rather than part of a DFW-HND itinerary.

On international flights one checked bag with no fee is permitted, and an additional checked bag without fee is allowed for Star Alliance Gold *G status, i.e. a total of two bags would be accepted without fee. However, on domestic flights, no checked bags are generally permitted, but *G status gives entitlement to one 'additional' checked bag, making for a total one free checked bag. It is possible that you would then be 'automatically' charged if you check in with two bags at DFW; you may be able to get an agent to see that it is part of an international itinerary.