This is correct. The OW benefit only applies to OW carriers.

While it is usually easy to get airlines to acknowledge DOT rules, sometimes it is a hassle with some airlines to get even the ticketed allowance. We were flying from KBP to the States in CW on BA and came back in WTP on BA via London but the last segment was on PS. On the outbound we had 3 bags(CW), but on the outbound the allowance was 2 bags (WTP). This is what the ticket said. For some reason the 3 bag allowance was not indicated for the return journey, although it was supposed to. PS said that they would honour what was on the ticket for their flight. The agents at LGW had no idea of the DOT rules and even told us that all they could see on the screen was 1 bag of each. They accepted 2 bags for each free of charge after we showed the ticket but I was surprised that he did not see it on the screen (or he simply told us untruth and wanted us to pay). But they did not even want to hear about the fact that our allowance was supposed to be per the first segment or that we even had an additional bag due to OW status.

So, while in a perfect world it all should work, sometimes it does not. And I am not sure on what basis I would dispute the charge if I had to pay to check-in a bank. May be it is easier to dispute such a charge if you paid with a card issued by a U.S. bank, but otherwise I can't see that being a success.