It pays to read the US DOT rule first. It expressly speaks to "reservations" and not "tickets". 14 CFR 259.5(b)(4) and it applies to BA on flights operated by BA to or from the US. Same title, Section 259.5(a). Thus, whether BA has ticketed the reservation is irrelevant (as it ought to be).
While it is true that the law would take precedence over a contract, in this case the law and the contract are not at odds.