It is certainly true that a carrier can decline another's reroute request, but it's also true that BA had the capacity to and should have either received confirmation or called to make certaint the reroute was confirmed by LH.

Sending a pax, whether F or not, off to another carrier to figure out whether the ticket was properly pushed is a dereliction.

The good thing about LH is that it follows the rules. The bad thing about LH is that it folows the rules. While it's easy to blame LH here, it's BA which could have alerted OP that his xFRA wasn't confirmed.